Test Bank for Calculus Early Transcendentals, 12th Edition Howard Anton, Irl C. Bivens, Stephen Davi

TEST BANK for Calculus Early Transcendentals, 12th Edition Howard Anton, Irl C. Bivens, Stephen Davis Chapter 1-15

Chapter 1 1.1

Limits and Continuity

Limits (An Intuitive Approach)

1) The function f (x) is shown in the graph:

Find

=

A) 2 B) -3 C) 3 D) -2 E) 0 Answer: B Diff: 1 Var: 1 Section: 1.1

1

2) Approximate the by evaluating f (x) =

at x = 4.5, 4.9, 4.99, 4.999, 5.5, 5.1, 5.01, and 5.001.

A) 5 B) 2.5 C) 11 D) 10 E) 12 Answer: D Diff: 2 Var: 1 Section: 1.1 3) Approximate the

by evaluating f (x) =

at appropriate values of x.

A) 1 B) 0 C) ∞ D) -∞ E) 10 Answer: C Diff: 1 Var: 1 Section: 1.1 4) Approximate the limit by evaluating f (x) =

at appropriate values of x.

A) 1 B) 11 C) -11 D) ∞ E) undefined Answer: B Diff: 2 Var: 1 Section: 1.1

2

=

5) Approximate the limit by evaluating f (x) =

at appropriate values of x.

A) 1 B) -6 C) D) ∞ E) undefined Answer: C Diff: 2 Var: 1 Section: 1.1 6) Approximate the limit by evaluating f (x) =

at appropriate values of x.

A) B) C) D) 0 E) ∞ Answer: A Diff: 2 Var: 1 Section: 1.1 7) Find the equation of the tangent line to the graph of y = 3 A) y = 15x + 12 B) y = 15x C) y = 12x D) y = 12x + 15 E) y = 5x + 12 Answer: A Diff: 3 Var: 1 Section: 1.1

3

at (-1, -3).

=

8) Given the function f (x) =

, for which value of c is

A) c = -4 B) c = -16 C) c = 0 D) c = 4 E) c = 16 Answer: D Diff: 1 Var: 1 Section: 1.1

4

and

9) Given the function f (x) =

, for which value of c is

and

A) c = -5 B) c = -25 C) c = 0 D) c = 5 E) c = 25 Answer: A Diff: 1 Var: 1 Section: 1.1 10) Given f (x) = tan (2x), which of the following is a vertical asymptote of f (x)?

A) x = π

B) x = C) x =

π

D) x =

π

E) x =

π

Answer: D Diff: 1 Var: 1 Section: 1.1

5

11) Given the function f (x) =

, for which value of c does

A) c = 0 B) c = 1 C) c = ±5 D) c = 10 E) c = 25 Answer: C Diff: 1 Var: 1 Section: 1.1

6

not exist?

f (x) = +∞?

12) For which of the following functions is A) f (x) = B) f (x) = C) f (x) =

+6

D) f (x) = E) f (x) = Answer: E Diff: 1 Var: 1 Section: 1.1

7

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.2

Computing Limits

1) Given that

f (x) = 5 and

g(x) = 10, find, if it exists,

A) -2500 B) 2500 C) 25 D) -50 E) It does not exist.

Answer: B Diff: 1 Var: 1 Section: 1.2 2)

5=

A) 9 B) -9 C) 5 D) 45 E) 0 Answer: C Diff: 1 Var: 1 Section: 1.2 3)

=

A) 9 B) -18 C) 81 D) -9 E) -81 Answer: B Diff: 2 Var: 1 Section: 1.2

8

4)

=

A) +∞ B) -∞ C) 0 D) It does not exist.

E) 8 Answer: D Diff: 3 Var: 1 Section: 1.2 5) Find

f (x)

where f (x) =

.

A) 6 B) 0 C) -6 D) ∞ E) It does not exist.

Answer: A Diff: 2 Var: 1 Section: 1.2 6)

=

A) 9 B) 0 C) ∞ D) -∞ E) It does not exist.

Answer: C Diff: 2 Var: 1 Section: 1.2

9

7)

=

A) 2 B) 0 C) ∞ D) -∞ E) It does not exist.

Answer: D Diff: 2 Var: 1 Section: 1.2 8)

=

A) 2 B) 0 C) ∞ D) -∞ E) It does not exist.

Answer: E Diff: 2 Var: 1 Section: 1.2

10

9) Use this graph of f (x)

to find

f (x) =

A) -1 B) -3 C) It does not exist.

D) 0 E) 2 Answer: C Diff: 1 Var: 1 Section: 1.2

11

10) Use this graph of f (x)

to find

f (x) =

A) ∞ B) 0 C) It does not exist.

D) 2 E) -3 Answer: E Diff: 2 Var: 1 Section: 1.2 11) Let f (x) =

, find

f (x) =

A) 256 B) 1 C) 2 D) 3 E) 0 Answer: C Diff: 3 Var: 1 Section: 1.2

12

12) Let f (x) =

, then

f (x) =

A) 14 B) 1024 C) 16 D) 0 E) It does not exist.

Answer: E Diff: 2 Var: 1 Section: 1.2 13)

=

A) 64 B) -16 C) 8 D) -64 E) -8 Answer: B Diff: 3 Var: 1 Section: 1.2 14) Given h(x) = 20, find

h(x).

A) 0 B) 1 C) 20 D) 2 E) 40 Answer: C Diff: 1 Var: 1 Section: 1.2 15) Given h(x) = 2x, find

h(x).

A) 0 B) 1 C) 2 D) 5 E) 10 Answer: E Diff: 1 Var: 1 Section: 1.2 13

16) Given g(x) =

, the limit of g(x) = -∞ for which of the following?

A) x→1⁻ B) x→1⁺ C) x→8⁻ D) x→8+ E) x→0 Answer: B Diff: 2 Var: 1 Section: 1.2 17) Given g(x) =

, the limit of g(x) = +∞ for which of the following?

A) x→-4⁻ B) x→-4⁺ C) x→-11⁻ D) x→-11⁺ E) x→0 Answer: B Diff: 2 Var: 1 Section: 1.2 18) Given g(x) =

, the limit of g(x) = -∞ for which of the following?

A) x→-4⁻ B) x→-4⁺ C) x→-9⁻ D) x→-9⁺ E) x→0 Answer: A Diff: 2 Var: 1 Section: 1.2 19) If f (x) = 9x and g(x) =

+ 2, what is

( f (x) + g(x))?

A) 11 B) 8 C) 32 D) 29 E) 92 Answer: A Diff: 1 Var: 1 Section: 1.2

14

20) Given h(x) = 9 , find

.

A) 3 B) 18 C) 108 D) 3888 E) 11,664 Answer: C Diff: 1 Var: 1 Section: 1.2

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

15

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.3

Limits at Infinity; End Behavior of a Function

1) A) 0 B) 4 C) 1 D) ∞ E) It does not exist.

Answer: A Diff: 1 Var: 1 Section: 1.3 2)

=

A) 0 B) -∞ C) ∞ D) 5 E) It does not exist.

Answer: D Diff: 2 Var: 1 Section: 1.3 3)

=

A) 0 B) +∞ C) -∞ D) 8 E) It does not exist.

Answer: B Diff: 2 Var: 1 Section: 1.3

16

4)

=

A) B) +∞ C) -∞ D) 4 E) It does not exist.

Answer: E Diff: 3 Var: 1 Section: 1.3 5) A) +∞ B) -∞ C) 25 D) 5 E) It does not exist.

Answer: D Diff: 3 Var: 1 Section: 1.3 6) A) -∞ B) ∞ C) 0 D) 3 E) It does not exist.

Answer: A Diff: 1 Var: 1 Section: 1.3

17

7) A) +∞ B) -∞ C) 0 D) E) It does not exist.

Answer: D Diff: 2 Var: 1 Section: 1.3

8) A) +∞ B) -∞ C) 0 D) 1 E) It does not exist.

Answer: D Diff: 2 Var: 1 Section: 1.3 9)

=

A) -2 B) 2 C) 0 D) -∞ E) +∞ Answer: B Diff: 2 Var: 1 Section: 1.3

18

10) For the function f (x) Shown in the graph below, find

A) 3 B) 1 C) 0 D) -3 E) Does not exist Answer: B Diff: 1 Var: 1 Section: 1.3

19

f (x).

11) For the function f (x) Shown in the graph below, find

A) 3 B) 1 C) 0 D) -3 E) Does not exist Answer: E Diff: 1 Var: 1 Section: 1.3

12) Given f (x) =

, find

f (x).

A) B) C) 4 D) E) 1 Answer: D Diff: 2 Var: 1 Section: 1.3

20

f (x).

13) Given f (x) =

-

, find

f (x).

A) 6 B) 12 C) 18 D) 0 E) Does not exist Answer: D Diff: 2 Var: 1 Section: 1.3

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

21

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.4

Limits (Discussed More Rigorously)

1) Find a least number δ such that

< ε if 0 <

< δ.

< ε if 0 <

< δ.

< ε if 0 <

< δ.

A) 1 B) 0.049 C) 0.007 D) 0.006 E) 0.009 Answer: C Diff: 2 Var: 1 Section: 1.4 2) Find a least number δ such that A) 0 B) 0.0043 C) 0.0046 D) 0.0053 E) 0.0057 Answer: B Diff: 2 Var: 1 Section: 1.4 3) Find a least number δ such that A) 0.01 B) 0.012 C) 0.013 D) 0.015 E) 0.016 Answer: C Diff: 2 Var: 1 Section: 1.4

22

5x - 2;

< ε if x > N.

4) Find a least positive number N such that A) 400 B) 20 C) 40 D) 100 E) 200 Answer: E Diff: 2 Var: 1 Section: 1.4 5) To prove that

(x - 4) = -2 a reasonable relationship between δ and ε would be

A) δ = 2ε B) δ = ε C) δ = D) δ = E) δ = ε - 4 Answer: B Diff: 2 Var: 1 Section: 1.4 6) To prove that

f (x) = 12, where a reasonable relationship between δ and ε would be

A) δ = 4ε B) δ = C) δ = 4ε + 9 D) δ = 3ε E) δ = Answer: B Diff: 3 Var: 1 Section: 1.4

23

7) If

+ 5 = 10 and ε = 0.007, find a largest positive number δ such that

if (Round to 3 decimal places.)

A) 0.067 B) 0.068 C) 0.069 D) 0.070 E) 0.071 Answer: D Diff: 3 Var: 1 Section: 1.4 8) If

4x = 8 and ε = 0.038, find a smallest positive number δ such that

if

A) 0.0075 B) 0.0085 C) 0.0095 D) 0.095 E) 0.038 Answer: C Diff: 1 Var: 1 Section: 1.4

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

24

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.5

Continuity

1) On the interval of [-4, 4], where is f not continuous?

A) -2 B) 0 and 2 C) -3 and 1 D) 3 E) Nowhere Answer: A Diff: 1 Var: 1 Section: 1.5 2) Find the x-coordinates for all points of discontinuity for f (x) = A) 3 and 7 B) 3 C) -7 and -3 D) -7 E) 7 Answer: A Diff: 3 Var: 1 Section: 1.5

25

.

3) Find the x-coordinates for all points of discontinuity for f (x) =

.

A) 0 B) -4 and 4 C) -4 D) 4 E) 3 Answer: C Diff: 2 Var: 1 Section: 1.5 4) Find the x-coordinates for all points of discontinuity for f (x) =

.

A) 2 B) 3 C) -2 D) 0 and 3 E) None exists.

Answer: A Diff: 1 Var: 1 Section: 1.5 5) Find the value of k, if possible, that will make the function continuous. f (x) = A) 1 B) 3 C) -3 D) -1 E) None exists.

Answer: D Diff: 3 Var: 1 Section: 1.5 6) Use the fact that 0.005.

A) 1.545 B) 1.555 C) 1.565 D) 1.575 E) 1.585 Answer: C Diff: 1 Var: 1 Section: 1.5

is a solution of

- 6 = 0 to approximate

26

with an error of at most

7) f (x) =

. Find the value for the constant k that will make the function

continuous everywhere.

A) 3 B) 4 C) 5 D) 6 E) 7 Answer: A Diff: 2 Var: 1 Section: 1.5 8) f (x) =

. Find the value for the constant k that will make the function

continuous everywhere.

A) -12 B) -11 C) -10 D) -9 E) -8 Answer: B Diff: 2 Var: 1 Section: 1.5 9) A point of discontinuity of f (x) =

is at

A) B) C) D) E) 2π Answer: D Diff: 3 Var: 1 Section: 1.5 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

27

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.6

Continuity of Trigonometric Functions

1) Find the limit.

=

A) 0 B) 1 C) -1 D) +∞ E) -∞ Answer: A Diff: 1 Var: 1 Section: 1.6 2) Find the limit.

=

A) 0 B) -1 C) 1 D) +∞ E) -∞ Answer: C Diff: 2 Var: 1 Section: 1.6 3) Find the limit.

=

A) 0 B) C) D) 1 E) +∞ Answer: C Diff: 2 Var: 1 Section: 1.6

28

4) Find the limit.

=

A) 1 B) 11 C) 0 D) +∞ E) -∞ Answer: C Diff: 2 Var: 1 Section: 1.6 5) Find the limit.

=

A) 3 B) C) 0 D) +∞ E) -∞ Answer: B Diff: 1 Var: 1 Section: 1.6 6) Find the limit.

=

A) 0 B) 1 C) 11 D) +∞ E) -∞ Answer: A Diff: 1 Var: 1 Section: 1.6

29

7) Find the limit.

=

A) 0 B) 1 C) D) +∞ E) -∞ Answer: C Diff: 2 Var: 1 Section: 1.6 8) Find the limit.

=

A) 0 B) C) D) +∞ E) -∞ Answer: B Diff: 2 Var: 1 Section: 1.6 9) Find the limit.

tan

=

A) 0 B) -1 C) 1 D) ∞ E) Does not exist Answer: E Diff: 2 Var: 1 Section: 1.6

30

10) Find the limit.

=

A) 0 B) -1 C) 1 D) +∞ E) -∞ Answer: A Diff: 3 Var: 1 Section: 1.6 11) Find all points of discontinuity, if any, for f (x) = A) 0 B) π C) 2π D) E) None exist Answer: E Diff: 3 Var: 1 Section: 1.6 12)

=

A) 0 B) 1 C) 5 D) ∞ E) It does not exist.

Answer: C Diff: 2 Var: 1 Section: 1.6

31

13)

=

A) 0 B) 1 C) D) 7 E) ∞ Answer: C Diff: 3 Var: 1 Section: 1.6

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 32

Chapter 1 1.7

Limits and Continuity

Inverse Trigonometric Functions

1) Given f (x) =

x, find

f (x).

x, find

f (x).

A) B) C) D) 0 E) 1 Answer: A Diff: 1 Var: 1 Section: 1.7 2) Given f (x) =

A) B) 0 C) D) E) 1 Answer: D Diff: 2 Var: 1 Section: 1.7

33

3) Given f (x) =

x, find

f (x).

A) 0 B) 1 C) D) E) Answer: E Diff: 1 Var: 1 Section: 1.7 4) At which of the following values is h(x) =

discontinuous?

A) 4 B) C) 3 D) E) 1 Answer: D Diff: 2 Var: 1 Section: 1.7 5) What is the exact value of

(-

)?

A) B) C) D) 0 E) 1 Answer: A Diff: 1 Var: 1 Section: 1.7 34

6) What is the exact value of A) π B) -π

(-1)?

C) D) 0 E) 1 Answer: A Diff: 1 Var: 1 Section: 1.7 7) What is the exact value of cos (

)?

A) B) C) D) E) 1 Answer: D Diff: 3 Var: 1 Section: 1.7 8) What is the exact value of cos (

)?

A) B) C) D) E) 1 Answer: C Diff: 3 Var: 1 Section: 1.7 35

9) Find A) B) C) 0 D) 1 E) Limit does not exist Answer: A Diff: 2 Var: 1 Section: 1.7 10) Find A)

π

B)

π

C)

π

D) 1 E) Limit does not exist Answer: C Diff: 2 Var: 1 Section: 1.7 11) Given

x=

π, find

(- x)

A) 7 B) -7 C) 1 D) E) Answer: B Diff: 1 Var: 1 Section: 1.7

36

12) For which value of x is A) 4.4 B) 2.2 C) -2.2

x not defined?

D) E) 1 Answer: D Diff: 1 Var: 1 Section: 1.7

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

37

Calculus Early Transcendentals, 12e (Anton) Chapter 1 Limits and Continuity 1.8

Exponential and Logarithmic Functions

1) Calculate: A) 25

=

B) C) D) E) -25 Answer: C Diff: 1 Var: 1 Section: 1.8 2) Use a calculating utility to approximate A) 2.5602 B) 2.5219 C) 3.2162 D) 2.5461 E) 535 Answer: D Diff: 1 Var: 1 Section: 1.8

. Round to four decimal places.

3) Use a calculating utility to approximate log 61.0. Round to four decimal places.

A) 1.8067 B) 1.7853 C) 1.8356 D) 1.7624 E) 4.1109 Answer: B Diff: 1 Var: 1 Section: 1.8

38

4) Find the exact value of

216.

A) B) C) 3 D) 36 E) 2.4495 Answer: C Diff: 2 Var: 1 Section: 1.8 5) Use a calculating utility to approximate ln 21 to four decimal places.

A) 3.0445 B) 2.8618 C) 2.7096 D) 2.5269 E) 3.2881 Answer: A Diff: 1 Var: 1 Section: 1.8 6) Rewrite the expression as a single logarithm. 8 log x - log 23 A) log 23 B) log C) log D) log 8 E) log 23x Answer: C Diff: 1 Var: 1 Section: 1.8 7) Solve

(x + 21) = 3 for x.

A) 979 B) 9 C) 1021 D) 51 E) 207 Answer: A Diff: 3 Var: 1 Section: 1.8 39

8) Solve for x. log A) 9 B) 8 C) 7 D) 11 E) 10 Answer: E Diff: 3 Var: 1 Section: 1.8

- log

=3

9) Solve = 17 for x to four decimal places.

A) 2.0437 B) -2.0437 C) -0.4893 D) 0.4893 E) -3.9277 Answer: B Diff: 2 Var: 1 Section: 1.8 10) Solve for x. 8 A) 9 B) -8 C) -9 D) 8 E) -17 Answer: B Diff: 3 Var: 1 Section: 1.8

+x

=0

40

11) This is the graph of

A) 4 + log(x - 3) B) 4 - log(x + 3) C) 4 + log(x + 3) D) 3 + log(x + 4) E) 3 + log(x - 4) Answer: C Diff: 2 Var: 1 Section: 1.8 12) Use a calculating utility and change of base formula to find

9. Round to 4 decimal

places.

A) -3.1699 B) 2.9163 C) 3.1699 D) 3.4552 E) -3.4552 Answer: C Diff: 2 Var: 1 Section: 1.8 13) The equation Q = 5 gives the mass Q in grams of a certain radioactive substance remaining after t hours. How much remains after 9 hours?

A) 3.6469 B) -3.6469 C) 4.2351 D) -3.9214 E) 3.9214 Answer: E Diff: 3 Var: 1 Section: 1.8

41

14) Solve for x.

(12 + x) = 2

A) 12 B) 1002 C) 118 D) 88 E) 112 Answer: D Diff: 3 Var: 1 Section: 1.8 15) Solve for x.

=6

A) 7 B) 6 C) 1 D) 0 E) 10 Answer: E Diff: 2 Var: 1 Section: 1.8 16) Given g(x) =

+ 4, find

g(x).

+ 2, find

g(x).

A) e + 4 B) 4 C) 1 D) E) 0 Answer: B Diff: 1 Var: 1 Section: 1.8 17) Given g(x) = A) e + 2 B) 5 C) 2 D) 3 E) 0 Answer: D Diff: 1 Var: 1 Section: 1.8

42

18) Given g(x) = 6

, find

g(x).

A) 6e B) 6 C) e D) 1 E) 0 Answer: A Diff: 2 Var: 1 Section: 1.8 19) Given f (x) = ln(7x) + 9, find

f (x).

A) 16 B) 7 C) 9 D) 10 E) 0 Answer: C Diff: 1 Var: 1 Section: 1.8 20) Given f (x) = ln(3x) + 1, find

f (x).

A) 4 B) 2 C) 1 D) 0 E) The limit does not exist Answer: E Diff: 1 Var: 1 Section: 1.8

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

43

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.1

Tangent Lines and Rates of Change

1) Find the average rate of change of y with respect to x for

over the interval

A) 1.102 B) -1.469 C) -1.531 D) -52.898 E) 8.816 Answer: B Diff: 1 Var: 1 Section: 2.1 2) Find the average rate of change of y with respect to x over the interval [1, 4].

A) 255 B) 428 C) 425 D) 319 E) 1275 Answer: C Diff: 1 Var: 1 Section: 2.1 3) Find the instantaneous rate of change of y = 7 A) 14 B) 70 C) 10 D) 35 E) 24 Answer: B Diff: 1 Var: 1 Section: 2.1

44

with respect to x at

= 5.

4) Find the instantaneous rate of change of

with respect to x at

A) -49 B) -0.9796 C) 0.0204 D) -0.0204 E) -7.0000 Answer: D Diff: 2 Var: 1 Section: 2.1 5) Find the instantaneous rate of change of y = 10

with respect to x at a general point

.

A) 60 B) 10 C) 10 D) 10 E) 60 Answer: E Diff: 1 Var: 1 Section: 2.1 6) Find the instantaneous rate of change of

with respect to x at a general point

A)

B)

C)

D)

E) Answer: C Diff: 2 Var: 1 Section: 2.1 45

.

7) Find the slope of the tangent line to the graph of A) -15

at a general point

.

-9

B) -3 C) -15 D) -3

-1

E) -3

-9

Answer: C Diff: 1 Var: 1 Section: 2.1 8) Use a graphing utility to graph y = - 7t + 10 on [0, 10]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is zero at what time?

Assume time is in seconds.

A) 6s B) 3s C) 3.5s D) 1.5s E) 7s Answer: C Diff: 2 Var: 1 Section: 2.1 9) A rock is dropped from a height of 240.1 meters and falls toward earth in a straight line. In t seconds the rock drops a distance of 4.9 meters. What is the instantaneous velocity downward when it hits the ground?

A) 282,475.249 meters/s B) 68.6 meters/s C) 34.3 meters/s D) 9.8 meters/s E) 14 meters/s Answer: B Diff: 1 Var: 1 Section: 2.1

46

10) An object moves in a straight line so that after t s its distance in mm from its original position is given by s = 5 + 8t. Its instantaneous velocity at t = 4s is A) 40 mm B) 168 mm C) 648 mm D) 48 mm E) 28 mm Answer: D Diff: 2 Var: 1 Section: 2.1 11) Find the instantaneous rate of change of y with respect to x at

= 4. y = 5

-7

= 16. y =

-2

A) 40 B) 33 C) 20 D) 47 E) 80 Answer: A Diff: 1 Var: 1 Section: 2.1 12) Find the instantaneous rate of change of y with respect to x at A) B) C) D) E) Answer: A Diff: 3 Var: 1 Section: 2.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

47

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.2

The Derivative Function

1) Find the equation of the tangent line to y = f (x) = 5x at x = 4.

A) y = 5x - 4 B) y = 5x C) y = -5x D) y = 5x + 4 E) y = 5x - 20 Answer: B Diff: 1 Var: 1 Section: 2.2 2) Find the equation of the tangent line to y = f (x) = A) y =

+

B) y =

+

C) y =

+

D) y = E) y =

+ +

Answer: B Diff: 3 Var: 1 Section: 2.2

48

+ 1 at x = 81.

3) Given y = 13

, find

.

A) B) C) D) E) Answer: D Diff: 2 Var: 1 Section: 2.2 4) Given the graph of f (x), for what value of x is

A) 1 B) 3 C) 2 D) -1 E) -3 Answer: A Diff: 2 Var: 1 Section: 2.2

49

(x) not defined?

5) Given the graph of f (x), for what value of x is

(x) not defined?

A) 4 B) 6 C) 5 D) -4 E) -6 Answer: D Diff: 2 Var: 1 Section: 2.2 6) Find f ′(t) if f (t) = -7 A) -35 - 8 B) -35 C) -35 - 8 D) -7 - 8 E) -35 Answer: E Diff: 1 Var: 1 Section: 2.2 7)

- 8.

represents the derivative of f (x) =

A) 16 B) 4 C) 1 D) 0 E) 12 Answer: B Diff: 1 Var: 1 Section: 2.2 50

at x = a. Find a.

8)

represents the derivative of f (x) =

at x = a. Find a.

A) 4 B) 256 C) 252 D) 1 E) 0 Answer: B Diff: 1 Var: 1 Section: 2.2 9) Find an equation for the tangent line to the curve y = A) y = 192x B) y = 192x - 1 C) y = 192 - 321 D) y = 192x - 321 E) y = 192 - 1 Answer: D Diff: 2 Var: 1 Section: 2.2 10) Let f (x) = sin x. Estimate

- 1 at (2, 63).

by using a graphing utility.

A) B) C) D) E) Answer: B Diff: 2 Var: 1 Section: 2.2

51

11) An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 4t + 4, , where t is time in seconds. How fast is the volume of the balloon increasing at t = 3s?

A) 12 ft3/s B) 16 ft3/s C) 1 ft3/s D) 0 ft3/s E) 4 ft3/s Answer: E Diff: 2 Var: 1 Section: 2.2 12) Given the graph of f (x), for what value of x is

A) 3 B) 5 C) 4 D) -3 E) 8 Answer: A Diff: 1 Var: 1 Section: 2.2 13) Find f ′(x) if f (x) = 8 .

A) 48 B) 48 C) 8 D) 6 E) Answer: B Diff: 1 Var: 1 Section: 2.2 52

(x) not defined?

14) Find f ′(x) if f (x) = 4

- 5x.

A) 24 - 5 B) 24 C) 24 - 5 D) 4 - 5 E) 24 Answer: A Diff: 1 Var: 1 Section: 2.2 15) Use the definition of the derivative to calculate f ′(x) if f (x) = -2 equation of the tangent line to the graph of f at A) y = -8x + 18 B) y = 8x - 18 C) y = -8x - 18 D) y = -

x+

E) y =

x-

+ 4x and find the

Answer: A Diff: 2 Var: 1 Section: 2.2 16) Use the definition of the derivative to calculate f ′(x) if f (x) = -4 of the normal line to the graph of f at x = 1.

A) y = -11x + 4 B) y = 11x + 4 C) y = -11x - 4 D) y = -

x+

E) y =

x-

Answer: E Diff: 2 Var: 1 Section: 2.2

53

- 3x and find the equation

17) Let y = A)

=-

B)

=

C)

=

D)

=-

E)

=-

. Use the definition of the derivative to find

.

Answer: A Diff: 2 Var: 1 Section: 2.2 18) Given that f (4) = 2 and f ′(4) = 5, find an equation for the tangent line to the graph of at the point where x = 4.

A) y = -5x + 18 B) y = 5x - 18 C) y = 5x + 18 D) y = 2x - 6 E) y = 2x + 6 Answer: B Diff: 3 Var: 1 Section: 2.2 19) The surface area of a sphere is given by S = 4π where r is the radius of the sphere. Find the instantaneous rate of change of S with respect to r when A) 12π B) 24π C) 36π D) 48π E) 72π Answer: D Diff: 1 Var: 1 Section: 2.2

54

20) Use the graph of f (x) shown to estimate

(1)

A) -4 B) 4 C) -2 D) 1 E) 6 Answer: A Diff: 1 Var: 1 Section: 2.2

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

55

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.3

Introduction to Techniques of Differentiation

1) Find

if y = 8 .

A) 64 B) 8 C) 64 D) 64x E) Answer: C Diff: 1 Var: 1 Section: 2.3 2) Find

if y =

.

A) B) C) 0 D) 1 E) Answer: C Diff: 1 Var: 1 Section: 2.3 3) Find

if y = 3(

- 3x + 3).

A) 3 - 3x - 9 B) 6 - 9 C) 18 - 9 D) 18 - 3 E) 3 - 3 Answer: C Diff: 1 Var: 1 Section: 2.3 56

4) y = 6

+ 8x + 7. Find

.

A) 12 B) 12x + 8 C) 6 D) 6x + 7 E) 7 Answer: A Diff: 2 Var: 1 Section: 2.3 5) y = 7 + 5x. Find y′′′.

A) 42 B) -420 C) -420 D) -420 +5 E) 42 +5 Answer: C Diff: 3 Var: 1 Section: 2.3 6) Use a graphing utility to locate all horizontal tangent lines to the curve A) x = 0 B) x = -12 and x = 0 C) x = -8 and x = 0 D) x = -8 E) x = -12 Answer: C Diff: 2 Var: 1 Section: 2.3

57

7) Find the x-coordinate of the point on the graph of y = the secant line that cuts the curve at x = 3 and at x = 5.

+ 2 where the tangent line is parallel to

A) B) 3127 C) 245 D) E) Answer: A Diff: 3 Var: 1 Section: 2.3 8) The position of a moving particle is given by s(t) = 2 velocity in m/s is given by

. Find the velocity at t = 2.

A) 128 m/s B) 16 m/s C) 32 m/s D) 64 m/s E) 57 m/s Answer: D Diff: 2 Var: 1 Section: 2.3

58

- 7 where t is time in seconds. The

9) Find

, if y =

.

A) 30 B) 5 - 5 C) D) 6 E)

+5

Answer: D Diff: 1 Var: 1 Section: 2.3

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

59

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.4

The Product and Quotient Rules

1) Given y =

, find

.

A) - 3 B) 3 C) D) E) -6 Answer: A Diff: 1 Var: 1 Section: 2.4 2) If y =

, find

.

A) B) C) D) E) Answer: B Diff: 2 Var: 1 Section: 2.4

60

3) If y =

,

(0) =

A) 0 B) C) D) E) Answer: D Diff: 2 Var: 1 Section: 2.4 4) g(x) = f (x). Find g′(3), given that f (3) = 5 and f ′(3) = 7.

A) 69 B) 39 C) 93 D) 153 E) 42 Answer: C Diff: 3 Var: 1 Section: 2.4 5) If y =

, find

(25).

A) B) C) D) E) Answer: E Diff: 3 Var: 1 Section: 2.4 61

6) Find

if y = -2(

- 4x)(3 +

).

A) -26 B) 46 C) 26 D) -74 E) -22 Answer: B Diff: 2 Var: 1 Section: 2.4 7) If f (4) = 2, (4) = 6, g(4) = 5, A) 19 B) 5 C) 3 D) 16 E) 4 Answer: B Diff: 1 Var: 1 Section: 2.4

(4) = 7, find

(4) if

8) If f (4) = 2, (4) = 6, g(4) = 5, A) 104 B) 94 C) 88 D) -50 E) -32 Answer: C Diff: 1 Var: 1 Section: 2.4

(4) = 7, find

(4) if F(x) = 2f (x)g(x).

62

9) If f (3) = 4,

(3) = 7, g(3) = 6,

(3) = 8, find

(3) if F(x) =

A) B) C) D) E) - 14 Answer: A Diff: 1 Var: 1 Section: 2.4 10) Find the equation of the tangent to the graph of y = A) y = -

x-

B) y =

x-

C) y = -

x+

D) y = -

x+

E) y = -

x-

Answer: E Diff: 3 Var: 1 Section: 2.4

63

at x = 2.

.

11) Find the equation of the line normal to the graph of y = A) y =

x+

B) y = -

x+

C) y =

x-

D) y =

x-1

E) y = -

x+1

at x = 2.

Answer: C Diff: 3 Var: 1 Section: 2.4

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

64

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.5

Derivatives of Trigonometric Functions

1) Find (x) if f (x) = A) 5 cos x sin x B) 5 cos x C) 5 sin x D) -5 cos x

cos x.

E) -5 sin x Answer: A Diff: 1 Var: 1 Section: 2.5 2) Find (x) if f (x) = sin x cot x.

A) sec x B) sin x C) cos x cot x - 1 D) -sin x E) cot x Answer: D Diff: 2 Var: 1 Section: 2.5 3) Find (x) if f (x) = A) 2 sec x + 2 tan x B) 2 sec x - 2 tan x C) -1 D) 1 E) 0 Answer: E Diff: 1 Var: 1 Section: 2.5

x+

x.

65

4) Find

if y = x cos x.

A) 2x cos x B) x sin x C) -2 sin x - x cos x D) sin x E) -2x cos x Answer: C Diff: 2 Var: 1 Section: 2.5 5) Find the equation of the line tangent to the graph of y = sin x at the point where x = 0.

A) y = cos x B) y = x C) y = -x D) y = 1 E) y = 1 Answer: E Diff: 2 Var: 1 Section: 2.5 6) Find the x-coordinates of all points in the interval [-2π, 2π] at which the graph of has a horizontal tangent line.

A) B) C) D) E) Answer: B Diff: 1 Var: 1 Section: 2.5

66

7) Find

cos x.

A) -sin x B) cos x C) sin x D) 0 E) -cos x Answer: E Diff: 2 Var: 1 Section: 2.5 8) Find all x-values on [0, 2π] where f (x) is not differentiable. f (x) = cos x cot x A)

,

B) 0, π, 2π C)

,

,

,

D) 0 E) none Answer: B Diff: 2 Var: 1 Section: 2.5 9) A rock at an elevation angle of θ is falling in a straight line. If at a given instant it has an angle of elevation of

and is a horizontal distance s from an observer, find the rate at which the rock

is falling with respect to θ.

A) B) s × C) D) E) s × sec Answer: B Diff: 2 Var: 1 Section: 2.5 67

10) If y =

cos x, find

.

A) 20 cos x - 10 sin x + cos x B) 20 cos x - 5 sin x cos x C) 20 cos x - 10 sin x cos x D) 20 cos x - 10 sin x E) 5 cos x sin x Answer: C Diff: 3 Var: 1 Section: 2.5 11) If y =

cos x, find

A) 8 cos x + sin x B) 8 sin x cos x C) 56 cos x - 16 sin x D) 56 cos x - 16 sin x E) 8 cos x sin x Answer: E Diff: 3 Var: 1 Section: 2.5 12) Find

.

cos x

if y = cos x.

A) -cos x B) cos x C) sin x D) -sin x E) sin x cos x Answer: A Diff: 1 Var: 1 Section: 2.5

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

68

Calculus Early Transcendentals, 12e (Anton) Chapter 2 The Derivative 2.6

The Chain Rule

1) f (x) =

.

(x) =

A)

B)

C) D)

E) Answer: D Diff: 2 Var: 1 Section: 2.6 2) f (x) =

.

(x) =

A) 26 B) 6 C) 156 D) 156 E) 26 Answer: C Diff: 2 Var: 1 Section: 2.6 3) f (x) = cos(5x). f ′(x) = A) -5 sin(cos 5x) B) - sin(5x) C) - 5 sin(x) D) -5 cos(5x) E) - cos(5x) Answer: A Diff: 2 Var: 1 Section: 2.6 69

4) If f (x) =

, then

A) 6

+

B) 6

+

(x) =

C) 6 D)

E) 6

+

Answer: E Diff: 3 Var: 1 Section: 2.6 5) y = tan(sin x). Find

.

A) - cos x (sin x) B) cos x (sin x) C) sin x (cos x) D) -sin x (cos x) E) - sin x (sin x) Answer: B Diff: 2 Var: 1 Section: 2.6 6) y =

cos(4x). Find

.

A) - 4 sin(4x) - 8 cos(4x) B) - 4 sin(4x) + cos(4x) C) - 4 sin(4x) + 8 cos(4x) D) - 4 sin(4x) E) 8 cos(4x) Answer: C Diff: 2 Var: 1 Section: 2.6

70

7) If y =

,

=

A) cos x B) - sin x C) - cos x D) sin x E) sin x cos x Answer: B Diff: 1 Var: 1 Section: 2.6 8) If y =

,

=

(Do not reduce any trig ratio identities.)

A)

B)

C)

D) E) Answer: B Diff: 3 Var: 1 Section: 2.6 9) y =

(π - 7θ). Find

.

A) - 21 cos(π - 7θ) (π - 7θ) B) - 21 cos(π + 7θ) (π + 7θ) C) - 21 (π - 7θ) sin(π - 7θ) D) -cos(π - 7θ) (π - 7θ) E) - 21 (π - 7θ) Answer: A Diff: 2 Var: 1 Section: 2.6

71

10) Find the value of the constant A in y = A sin 6t so that

+ 4y = sin 6t.

A) B) C) D) 32 E) 40 Answer: C Diff: 3 Var: 1 Section: 2.6 11) Find

(x) if f (x) =

.

A) 11 B) C) 44 D) 44 E) 11 Answer: D Diff: 2 Var: 1 Section: 2.6 12) Find

if y = sin(cos x).

A) -sin x cos(sin x) B) -cos(cos x) C) sin x cos(cos x) D) -sin x cos(cos x) E) cos(sin x) Answer: D Diff: 2 Var: 1 Section: 2.6

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

72

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.1 1) If

Implicit Differentiation = 2x, find

at the point (32, 8).

A) B) C) 2 D) E) 8 Answer: A Diff: 1 Var: 1 Section: 3.1 2) Given

+

= 25, find

at the point (4, 3).

A) B) C) D) E) Answer: A Diff: 1 Var: 1 Section: 3.1

73

3) Given

- 2x, find

A)

=5

B)

=5

-2

C)

=5

+2

D)

=5

-1

E)

=5

+1

.

Answer: A Diff: 1 Var: 1 Section: 3.1 4) Given

+

= 2x, use implicit differentiation to find

A) B) C) D) E) Answer: D Diff: 1 Var: 1 Section: 3.1

74

at (1,1).

5) Given 7xy = A)

=

B)

=

C)

=

D)

=

E)

=

, use implicit differentiation to find

.

Answer: A Diff: 1 Var: 1 Section: 3.1 6) Given 4x + cos(y) = 2 , use implicit differentiation to find A)

=

B)

=

C)

=

D)

=

E)

=

Answer: A Diff: 2 Var: 1 Section: 3.1

75

.

7) Use implicit differentiation to find A)

=

B)

=

C)

=

D)

=

E)

=

given sin(xy) = 5 .

Answer: B Diff: 2 Var: 1 Section: 3.1 8) Given tan(5y) = 7 , use implicit differentiation to find A)

=

B)

=

C)

=

D)

=

E)

=

.

Answer: A Diff: 2 Var: 1 Section: 3.1 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

76

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.2

Derivatives of Logarithmic Functions

1) If y = ln 8x find

.

A) B) C) D) E) Answer: C Diff: 1 Var: 1 Section: 3.2 2) If y = ln(cos x) find

.

A) - tan x B) tan x C) D) E) - sin x Answer: A Diff: 2 Var: 1 Section: 3.2

77

3) Given y = -2 ln( ), find A)

=

B)

=

C)

=

D)

=

E)

=

Answer: C Diff: 2 Var: 1 Section: 3.2 4) Given

- ln(xy) = 6, use implicit differentiation to find

A)

=4 y-

B)

= 24 y -

C)

=4 y-

D)

=4 y+

E)

= 24 y +

Answer: A Diff: 2 Var: 1 Section: 3.2

78

.

5) y = ln(cot x). Find

.

A) sin x cos x B) C) x D) cot x E) Answer: E Diff: 2 Var: 1 Section: 3.2 6) y = ln(5x). For n ≥ 2,

=

A)

B)

C)

D)

E) Answer: C Diff: 3 Var: 1 Section: 3.2

79

7) Given 3x ln y = -2, use implicit differentiation to find A)

=-

ln y

B)

=-

ln y

C)

= -2 -

ln y

D)

= -2 +

ln y

E)

= -2 -

ln y

Answer: B Diff: 2 Var: 1 Section: 3.2 8) Given f (x) = 3x ln(sin x) + 1 , find A) 3x cot x + 3ln(sin x) + 6

(x).

B) 3x cot x - 3ln(sin x) + 6 C) 3x tan x + 3ln(sin x) + 6 D) 3x cot x + 3ln(cos x) + 6 E) 3x cot x - 3ln(cos x) + 6 Answer: A Diff: 2 Var: 1 Section: 3.2

80

.

9) Given y = 5ln(6x), find A)

=

B)

=

C)

=

D)

=

E)

=

.

Answer: E Diff: 2 Var: 1 Section: 3.2 10) Given y = 2x ln( ), find A)

= 8 + 2 ln( )

B)

= 8 + 8 ln( )

C)

= 8 - 2 ln( )

D)

= 2x + 4 ln( )

E)

= 2x + 8 ln( )

.

Answer: A Diff: 2 Var: 1 Section: 3.2

81

11) Given y =

ln(15x), find

at x = 1.

A) 4ln(15) B) C) 4ln(15) - 1 D) 4ln(15) + 1 E)

-1

Answer: D Diff: 2 Var: 1 Section: 3.2

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

82

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.3

Derivatives of Exponential and Inverse Trigonometric Functions

1) Which one of the following functions is one-to-one on its natural domain?

A) f (x) = -4 + cos (6x) B) f (x) = - 4x + 3 C) f (x) = D) f (x) =

-4

+3

+3

E) f (x) = -4 Answer: A Diff: 1 Var: 1 Section: 3.3 2) Given that f (x) = 5 A) 2 B) 7

- 3x - 2 and that f (1) = 0, find (

)'(0).

+ 4x - 1 and that f (1) = 4, find (

)'(4).

C) D) -7 E) Answer: C Diff: 1 Var: 1 Section: 3.3 3) Given that f (x) = A) 3 B) 5 C) D) 7 E) Answer: E Diff: 1 Var: 1 Section: 3.3

83

4) Given y = A)

=9

B)

=9

C)

=9

D)

= 9x

E)

= 9x

- 2, find

.

-2

Answer: A Diff: 1 Var: 1 Section: 3.3 5) Given y =

, find

A)

=7

B)

=

C)

= (7

D)

=(

-

E)

=7

ln x

+

.

) )

Answer: C Diff: 1 Var: 1 Section: 3.3

84

6) Given y = sin(5

), find

A)

= 15cos(5

)

B)

= 15

cos(5

C)

= cos(5

)

D)

= 15sin(5

) + cos(5

E)

= 15sin(5

)

.

)

)

Answer: B Diff: 1 Var: 1 Section: 3.3 7) Given y = 2

(3x), find

.

A)

B)

C)

D)

E) Answer: A Diff: 1 Var: 1 Section: 3.3

85

8) Given y = 4

( ), find

.

A) B)

C)

D)

E) Answer: C Diff: 1 Var: 1 Section: 3.3 9) Given f (x) =

, find

(x).

A) 6 B) - 3 C) D) E) - 4 Answer: B Diff: 1 Var: 1 Section: 3.3

86

10) Given f (x) =

(5

), find

(0)

A) B) C) 0 D) E) Answer: E Diff: 1 Var: 1 Section: 3.3

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

87

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.4

Related Rates

1) The volume of a cylinder is given by V = π h. Find

in terms of

. (Assume that r is a

constant.)

A) πr2 B) 1 C) πr D) r2 E) π Answer: A Diff: 1 Var: 1 Section: 3.4 2) A 10-ft ladder rests against a wall at π/5 radians. If it were to begin to slip, when the bottom of the ladder is moving at 0.09 ft/s, how fast would the top of the ladder be moving down the wall?

(How fast would the height of the upper end of the ladder on the side of the wall be changing?)

A) 0.118 ft/s B) 0.115 ft/s C) 0.113 ft/s D) 0.124 ft/s E) 0.132 ft/s Answer: D Diff: 2 Var: 1 Section: 3.4

88

3) Suppose z = A) 5

+

. Then dz/dt =

+3

B) 5

+3

C) 15 D) 5x E)

+ 3y +

Answer: B Diff: 2 Var: 1 Section: 3.4 4) The power in watts for a circuit is given by P = R. How fast is the power changing if the resistance, R, of the circuit is 800 Ω, the current, I, is 3.6 A, and the current is decreasing with respect to time at a rate of 0.02 A/s. (Assume R is a constant.)

A) 115.2 w/s B) 5760 w/s C) 28.8 w/s D) 414.72 w/s E) -115.2 w/s Answer: E Diff: 2 Var: 1 Section: 3.4 5) Gravitational force is inversely proportional to the distance between two objects squared. If at a distance d = 4 m, how fast is the force diminishing if the objects are moving away from each other at 0.9 m/s?

A) 5.4 N/s B) -5.4 N/s C) -6 N/s D) 6 N/s E) 0 N/s Answer: B Diff: 2 Var: 1 Section: 3.4

89

6) A point P is moving along a curve whose equation is increasing at a rate of 2 units/s. How fast is x changing?

A) 1.765 units/s B) 510 units/s C) 1.267 units/s D) 2.267 units/s E) 3.267 units/s Answer: D Diff: 3 Var: 1 Section: 3.4

When

y is

7) The number of board feet of lumber in a log that is 14 feet long is given by the formula , where D is the diameter of the tree in inches. In a tree that will produce a 14 foot log and has a current diameter of 26 inches, the diameter is changing at a rate of 1.2 inches per year. How fast is the volume increasing?

A) 23.5 ft3/year B) 14.1 ft3/year C) 28.2 ft3/year D) 11.8 ft3/year E) 247.0 ft3/year Answer: C Diff: 2 Var: 1 Section: 3.4

90

8) The elastic modulus of a piece of steel rod under a load of 1100 pounds, is given by the formula L is the original, unloaded, length in inches, A is the cross-sectional area in square inches, and l is the elongation due to a load in inches. A 48 inch long steel rod is with a cross-sectional area of A = 2.8 square inches, is stretching 0.004 inches under a load of 1100 pounds. Due to changes in temperature, the elastic modulus E of the rod is changing. Find the rate of change of the elastic modulus if the elongation is currently 0.004 and is changing at a rate of 0.00032 in/s.

A) -377,143 lb/in2 B) 377,143 lb/in2 C) -1,178,571,429 lb/in2 D) -1509 lb/in2 E) 1509 lb/in2 Answer: A Diff: 3 Var: 1 Section: 3.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

91

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.5

Local Linear Approximation; Differentials

1) Find the local linear approximation of f (x) = 5 A) y =

x + 10

B) y =

x - 10

C) y = -

x + 10

D) y =

x+

E) y =

x-

at

= 16.

at

= 36 to approximate f (36.1).

Answer: A Diff: 1 Var: 1 Section: 3.5 2) Find the local linear approximation of f (x) = 7 A) B) C) D) E) Answer: A Diff: 1 Var: 1 Section: 3.5

92

3) Find the local linear approximation of f (x) = 2sin x + 4x at

= 0.

A) y = 8x B) y = 6x - 2 C) y = 6x - 4 D) y = 8x - 2 E) y = 6x Answer: A Diff: 1 Var: 1 Section: 3.5 4) The diameter of a circular metal plate is measured with a percentage error within 0.2%.

Estimate the percentage error in calculating the area of the plate.

A) 0.2% B) 0.4% C) 0.6% D) 0.8% E) 1.2% Answer: A Diff: 1 Var: 1 Section: 3.5 5) The radius of a glass sphere is measured with a percentage error within 0.1%. Estimate the percentage error in calculating the volume of the sphere.

A) 0.1% B) 0.2% C) 0.3% D) 0.4% E) 0.6% Answer: A Diff: 1 Var: 1 Section: 3.5 6) Find an equation for the local linear approximation to y = 3 - 4 A) y = -16x + 23 B) y = -16x + 15 C) y = 16x + 23 D) y = -12x + 23 E) y = -16x + 17 Answer: A Diff: 1 Var: 1 Section: 3.5

93

at x = 1.

7) Use the differential dy to approximate △ y = y = Round your answer to the nearest hundredth.

A) 0.47 B) 0.48 C) 0.51 D) 0.53 E) 0.54 Answer: A Diff: 1 Var: 1 Section: 3.5

, when x changes from 2 to 2.04.

8) What is the formula for the local linear approximation for f (x) = -3 A) y = -

x-5

B) y =

x-4

C) y =

x+5

D) y = -

x+4

E) y = -

x+5

Answer: A Diff: 1 Var: 1 Section: 3.5 9) What is the formula for the local linear approximation of f (x) = 4 tan (1x) + 2 at = 0?

A) y = 9x + 2 B) y = 2x + 2 C) y = -2x + 2 D) y = -2x - 2 E) y = 6x + 2 Answer: A Diff: 1 Var: 1 Section: 3.5

94

at

= 8?

10) Use a local linear approximation of f (x) = 2ln x at

= 1 to estimate the value of

A) 0.08 B) 0.1 C) 0.13 D) 0.14 E) 0.25 Answer: A Diff: 1 Var: 1 Section: 3.5

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

95

Calculus Early Transcendentals, 12e (Anton) Chapter 3 Topics in Differentiation 3.6

L'Hôpital's Rule; Indeterminate Forms

1) For which limit does L'Hôpital's rule apply?

A) B) C) D) E)

cos

Answer: A Diff: 1 Var: 1 Section: 3.6 2) Evaluate the limit: A) 3 B) C) D) 0 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6

96

3) Evaluate the limit: A) 0 B) 8 C) 40 D) E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 4) Evaluate the limit: A) B) C) D) 0 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 5) Evaluate the limit: A) B) C) D) E) 0 Answer: A Diff: 1 Var: 1 Section: 3.6 97

6) Evaluate the limit: A) B) C) D) E) 0 Answer: A Diff: 1 Var: 1 Section: 3.6 7) Evaluate the limit: A) -4 B) 6 C) D) 0 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 8) Evaluate the limit: A) 3 B) 1 C) D) 0 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6

98

9) Evaluate the limit:

A) B) C) D) 2 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 10) Evaluate the limit: A) 0 B) 3 C) D) 15 E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 11) Evaluate the limit: A) 0 B) 2 C) D) 2e E) does not exist Answer: A Diff: 1 Var: 1 Section: 3.6 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

99

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.1

Analysis of Functions I: Increase, Decrease, and Concavity

1) The largest interval over which f is increasing for f (x) = A) [-5, 5] B) [5, ∞ ) C) (-∞ , -5] D) (-∞ , 5] E) [-5, ∞ ) Answer: B Diff: 2 Var: 1 Section: 4.1

is

2) The largest interval over which f is increasing for f (x) = A) (-∞ , -9] B) [9, ∞ ) C) (-∞ , ∞ ) D) [-9, ∞ ) E) (-∞ , 9] Answer: C Diff: 1 Var: 1 Section: 4.1

- 9 is

3) The largest interval over which f is increasing for f (x) = A) [8, ∞ ) B) (-∞ , 8] C) (-∞ , ∞ ) D) nowhere E) (-8, ∞ ) Answer: A Diff: 1 Var: 1 Section: 4.1

is

4) The largest open interval over which f is concave up for f (x) = A) (3, ∞ ) B) (-∞ , 3) C) (-∞ , ∞ ) D) (-3, 3) E) nowhere Answer: B Diff: 2 Var: 1 Section: 4.1 100

is

5) The largest open interval over which f is concave up for f (x) = 2

+3

A) B) C) D) E) (-∞, ∞) Answer: C Diff: 2 Var: 1 Section: 4.1 6) The function f (x) =

has a point of inflection with an x-coordinate of

A) B) C) 0 D) 1 E) None exist Answer: C Diff: 1 Var: 1 Section: 4.1 7) The function f (x) = A) 10 B) -10 C) 9 D) 0 E) None exist Answer: D Diff: 1 Var: 1 Section: 4.1

- 10 has a point of inflection with an x-coordinate of

101

- 8x + 7 is

is decreasing on [0, 2π].

8) Use a graphing utility to determine where f (x) = cos A) [0, π] B) C) D) E) [π, 2π] Answer: B Diff: 2 Var: 1 Section: 4.1 9) Answer true or false. tan(-2x + 6) has a point of inflection on

.

Answer: TRUE Diff: 1 Var: 1 Section: 4.1 10) f (x) = -5 decimal places.)

A) (-1.581, 1.581) B) (0, ∞) C) (-∞, ∞) D) (-0.913, 0.913) E) (-1.118, 1.118) Answer: D Diff: 2 Var: 1 Section: 4.1

- 12 is concave down on the interval I =

102

(Approximate your answer to 3

11) The function f (x) =

has

A) points of inflection at x = -16 and x = 16 B) points of inflection at x = -4 and x = 4 C) points of inflection at x = 0 D) no point of inflection E) points of inflection at x = 4 Answer: D Diff: 3 Var: 1 Section: 4.1

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

103

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.2

Analysis of Functions II: Relative Extrema; Graphing Polynomials

1) Determine the x-coordinate of each stationary point of f (x) = 3 A) x = 2 B) x = 4 and x = 0 C) x = 2 and x = 0 D) x = -4 E) None exist Answer: A Diff: 1 Var: 1 Section: 4.2

- 12x.

2) Determine the x-coordinate of each critical point of f (x) = A) 0 B) 3 C) 9 D) -3 E) None exist Answer: B Diff: 2 Var: 1 Section: 4.2

.

3) f (x) = + 6x + 9 has a A) relative maximum at x = -3.

B) relative minimum at x = -3.

C) relative maximum at x = -6.

D) relative minimum at x = -6.

E) relative maximum at x = -9.

Answer: B Diff: 2 Var: 1 Section: 4.2 4) f (x) = 1.3x on 0 < x < 2π has A) a relative maximum only.

B) a relative minimum only.

C) both a relative maximum and a relative minimum.

D) neither a relative maximum nor a relative minimum.

E) cannot be determined.

Answer: C Diff: 3 Var: 1 Section: 4.2

104

5) f (x) = - 8 has A) a relative maximum at x = 6 and no relative minimum.

B) no relative maximum and a relative minimum at x = 6.

C) a relative maximum at x = 0 and a relative minimum at x = 6.

D) a relative maximum at x = 6 and a relative minimum at x = 0.

E) a relative maximum at x = 0 and no relative minimum.

Answer: B Diff: 2 Var: 1 Section: 4.2 6) f (x) = has A) a relative minimum at x = 0.

B) a relative maximum at x = 0.

C) a relative maximum at x = 8.

D) a relative minimum at x = 8.

E) a relative minimum at x = -8.

Answer: D Diff: 1 Var: 1 Section: 4.2 7) f (x) = has A) no relative maximum and a relative minimum at x = 3.

B) a relative maximum at x = 3 and no relative minimum.

C) relative minima at x = -3 and x = 3; a relative maximum at x = 0.

D) relative maxima at x = -3 and x = 3; a relative minimum at x = 0.

E) no relative extrema.

Answer: C Diff: 2 Var: 1 Section: 4.2 8) f (x) = - 8 has A) a relative maximum only.

B) a relative minimum only.

C) both a relative maximum and a relative minimum.

D) neither a relative maximum nor a relative minimum.

E) cannot be determined.

Answer: B Diff: 1 Var: 1 Section: 4.2

105

9) On the interval (0, 2π), f (x) = has A) a relative maximum only.

B) a relative minimum only.

C) both a relative maximum and a relative minimum.

D) no relative extrema.

E) cannot be determined.

Answer: C Diff: 2 Var: 1 Section: 4.2 10) The polynomial function - 12x + 13 has A) one stationary point that is at x = 12.

B) one stationary point that is at x = -6.

C) two stationary points, one at x = 0 and one at x = 12.

D) two stationary points, one at x = 6 and one at x = -6.

E) one stationary point that is at x = 6.

Answer: E Diff: 2 Var: 1 Section: 4.2 11) The rational function f (x) =

has

A) a horizontal asymptote at y = 2.

B) a horizontal asymptote at y = 5.

C) a horizontal asymptote at y = -2.

D) a horizontal asymptote at y = 0.

E) no horizontal asymptote.

Answer: D Diff: 3 Var: 1 Section: 4.2 12) The rational function f (x) =

has

A) a stationary point at x = 1.

B) a stationary point at x = -1.

C) two stationary points at approximately x = -1.158 and x = 1.158.

D) three stationary points approximately at x = 0, x = -1.158 and x = 1.158.

E) no stationary points.

Answer: C Diff: 3 Var: 1 Section: 4.2

106

13) Use a graphing utility to graph f (x) = have?

A) 0 B) 1 C) 2 D) 3 E) 4 Answer: B Diff: 1 Var: 1 Section: 4.2

. How many points of inflection does the function

14) Use a graphing utility to graph f (x) = have?

A) 0 B) 1 C) 2 D) 3 E) 4 Answer: A Diff: 1 Var: 1 Section: 4.2

. How many points of inflection does the function

15) Determine which function is graphed.

A) f (x) = B) f (x) = C) f (x) = D) f (x) = E) f (x) = Answer: C Diff: 2 Var: 1 Section: 4.2

107

16) Use a graphing utility to generate the graph of f (x) = determine the x-coordinates of all relative extrema on maxima or relative minima.

A) There is a relative maximum at x = 3.

B) There is a relative minimum at x = 0.

C) There is a relative maximum at x = 0.

D) There is a relative minimum at x = 3.

E) There are no relative extrema.

Answer: D Diff: 3 Var: 1 Section: 4.2

- 6 + 11 - 12x + 6, then and identify them as relative

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

108

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.3

Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents

1) Evaluate

.

A) 0 B) 1 C) +∞ D) E) It does not exist Answer: A Diff: 1 Var: 1 Section: 4.3 2) A) 0 B) 1 C) +∞ D) It does not exist E) Answer: C Diff: 1 Var: 1 Section: 4.3 3) Given y =

. Find any points of inflection.

A) B) (0, 0) C) (1, 1) D) (±1, 1) E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3

109

4) Given y =

. Find any stationary points.

A) (0, 0) B) C) (1, 1) D) (±1, 1) E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3 5) Given y =

. Find any horizontal and vertical asymptotes.

A) x = 1 B) y = 1 C) y = 0 D) x = 0 E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3 6) Given y =

, find any stationary points.

A) Relative maximum at (0, 0) B) Relative minimum at (0, 0) C) Relative maximum at (±2, 2) D) Relative minimum at (±2, 2) E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3

110

7) Given y =

, find any points of inflection.

A) (0, 0) B) (±5, 5) C) (0, 0) and (±5, 5) D) (±16, 16) E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3 8) Given y =

, find any find any horizontal and vertical asymptotes.

A) Horizontal asymptote at y = 3 Vertical asymptotes at x = ±4 B) Vertical asymptotes at x = ±4 C) Horizontal asymptotes at y = 3 and y = 0 D) Horizontal asymptote at y = 3 and y = 0 Vertical asymptotes at x = ±4 E) None exist Answer: A Diff: 2 Var: 1 Section: 4.3 9) Given y = (x + 7), find any stationary points which may or may not exist. Approximate answers to 4 decimal places.

A) Relative maximum at (-2.8, ≈8.3436) Relative minimum at (0, 0) Inflection point at (1.4, ≈10.5123) B) Relative maximum at (-2.8, ≈8.3436) C) Relative minimum at (0, 0) D) Relative minimum at (-2.8, ≈8.3436) E) Relative maximum at (0, 0) Answer: A Diff: 3 Var: 1 Section: 4.3

111

10) Given y = (x + 2), find any inflection points which may or may not exist. Approximate answers to 4 decimal places.

A) (0.4, ≈1.3029) B) (0, 0) C) (-0.8, ≈1.0341) D) (0, 0) and (0.4, ≈1.3029) E) None exist Answer: A Diff: 3 Var: 1 Section: 4.3 11) Given y = (x + 7), find any cusps which may or may not exist. Approximate answers to 4 decimal places.

A) (0, 0) B) (-2.8, ≈8.3436) C) (1.4, ≈10.5123) D) (0, 0) and (1.4, ≈10.5123) E) None exist Answer: A Diff: 3 Var: 1 Section: 4.3

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

112

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.4

Absolute Maxima and Minima

1) Find the absolute maximum of the function f (x) = 7 A) -1 B) -7 C) 0 D) 7 E) 21 Answer: D Diff: 1 Var: 1 Section: 4.4

- 14x on the closed interval [-1, 2].

2) Find the absolute minimum of the function f (x) = 6 A) -5 B) -6 C) 0 D) 6 E) 210 Answer: B Diff: 1 Var: 1 Section: 4.4

- 12x on the closed interval [-5, 2].

3) Find the absolute maximum of the function f (x) = 2 A) -4 B) -10 C) 0 D) 4 E) -2 Answer: D Diff: 1 Var: 1 Section: 4.4

+0

- 6x on the closed interval [-1, 2].

4) Find the absolute minimum of the function f (x) = 2 A) -4 B) -10 C) 0 D) 4 E) -2 Answer: A Diff: 1 Var: 1 Section: 4.4

+0

- 6x on the closed interval [-1, 2].

5) Find the absolute maximum of the function f (x) = 5x - 10 sin x on the closed interval [0, π].

113

A) 0 B) 5 C) 5 D) 5π E) 5 Answer: D Diff: 2 Var: 1 Section: 4.4 6) Find the absolute minimum of the function f (x) = 3x - 6 sin x on the closed interval [0, π].

A) 0 B) 3 C) 3 D) 3π E) 3 Answer: C Diff: 2 Var: 1 Section: 4.4 7) Find the absolute maximum of the function f (x) = A) 7 B) 4 C) 3 D) 1 E) 0 Answer: A Diff: 2 Var: 1 Section: 4.4

114

+ 3 on the closed interval [2, 11].

8) Find the absolute minimum of the function f (x) = A) 1 B) 4 C) 5 D) 6 E) There is no absolute minimum Answer: C Diff: 2 Var: 1 Section: 4.4

+ 5 on the closed interval [2, 11].

9) Find the absolute minimum of the function f (x) = A) -1 B) -5 C) 0 D) 5 E) There is no absolute minimum Answer: B Diff: 2 Var: 1 Section: 4.4

+ 10

on the interval [0, ∞].

10) Find the absolute maximum of the function f (x) = A) 10 B) 5 C) 0 D) -5 E) There is no absolute maximum Answer: E Diff: 2 Var: 1 Section: 4.4

+ 10

on the interval [0, ∞].

11) Find the absolute minimum of the function f (x) =

on the interval [0, 4].

A) 0 B) 2 C) 4 D) 8 E) There is no absolute minimum Answer: B Diff: 2 Var: 1 Section: 4.4

115

12) Find the absolute maximum of the function f (x) =

on the interval [0, 3].

A) 0 B) C) 3 D) 8 E) There is no absolute maximum Answer: E Diff: 2 Var: 1 Section: 4.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

116

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.5

Applied Maximum and Minimum Problems

1) Express the number 18 as the sum of two nonnegative numbers whose product is as large as possible.

A) 0, 18 B) 9, 9 C) 9, 9 D) 4, 14 E) 21, 0 Answer: C Diff: 1 Var: 1 Section: 4.5 2) A right triangle has a perimeter of 94. What are the lengths of each side if the area contained within the triangle is to be maximized?

A)

,

,

,

B) 43, 43, 8 C) 94 - 47 , 94 - 47 D) 47 - 94 , 47 - 94 E) 37, 37, 20 Answer: C Diff: 3 Var: 1 Section: 4.5

, -94 + 94 , -47 + 47

3) A rectangular sheet of cardboard 80 cm by 93 cm is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut to obtain the largest possible volume?

A) B) C) D) 4 E) Answer: B Diff: 2 Var: 1 Section: 4.5 117

4) Suppose that the number of bacteria present in a culture bacteria at time t is given by Find the smallest number of bacteria in the culture during the time interval A) 95,000 B) 456,000 C) 931,000 D) 247,000 E) 836,000 Answer: D Diff: 2 Var: 1 Section: 4.5 5) An object moves a distance s away from the origin according to the equation where At what time is the object farthest from the origin?

A) 0 B) 8 C) 5 D) E) Answer: B Diff: 1 Var: 1 Section: 4.5 6) An electrical generator produces a current in amperes starting at s and running until that is given by 5cos(4t). Find the maximum current produced.

A) 5A B) 0A C) 2πA D)

A

E)

A

Answer: A Diff: 1 Var: 1 Section: 4.5

118

7) A storm is passing with the wind speed in mph changing over time according to for Find the highest wind speed that occurs.

A) 652 mph B) 644 mph C) 1292 mph D) 284 mph E) 4 mph Answer: E Diff: 2 Var: 1 Section: 4.5 8) A company has a cost of operation function given by Find the minimum cost of operation.

A) 1500 B) 1450 C) 2900 D) 1499.96 E) 1401 Answer: B Diff: 2 Var: 1 Section: 4.5 9) Find the point on the curve A) (0, 49) B) (0, 7) C) (0, 8) D) (7, 0) E) (49, 0) Answer: B Diff: 1 Var: 1 Section: 4.5

+

for

= 49 closest to

10) For a triangle with sides 5 m, 12 m, and 13 m, the smallest circle that contains the triangle has a diameter of A) 5 m B) 12 m C) 13 m D) 17 m E) 15 m Answer: C Diff: 3 Var: 1 Section: 4.5

119

11) Two numbers sum to 210. Find the two numbers whose product is maximum.

A) 35, 204 B) 7, 203 C) 30, 205 D) 105, 105 E) 42, 168 Answer: D Diff: 1 Var: 1 Section: 4.5 12) A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side.

Two kinds of fencing will be used with heavy duty fencing selling for $6 a foot on the side opposite the wall. The two remaining sides will use standard fencing selling for $5 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $44,640?

A) heavy duty = 3720 feet and standard = 2232 feet B) heavy duty = 4080 feet and standard = 2016 feet C) heavy duty = 4050 feet and standard = 2572 feet D) heavy duty = 4050 feet and standard = 2034 feet E) heavy duty = 2562 feet and standard = 3380 feet Answer: A Diff: 3 Var: 1 Section: 4.5 13) A divided field is to be constructed with 6040 feet of fence as shown.

For what value of y will the area be a maximum?

A) 755 feet B) 1510 feet C) 78 feet D) 865 feet E) 1356 feet Answer: A Diff: 2 Var: 1 Section: 4.5

120

14) Find the area of the largest possible isosceles triangle with 2 sides equal to 12 inches.

A) 72 square inches B) 12 square inches C) 6 square inches D) 24 square inches E) 48 square inches Answer: A Diff: 2 Var: 1 Section: 4.5 15) A lighthouse is 4 miles off a straight coast and a town is located 10 miles down the seacoast.

Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at the rate of 5 miles/hour on water and 13 miles/hour over land, how far from the town should a dock be constructed for shipment of supplies?

A) 8 miles B)

miles

C) 2

miles

D) 1

miles

E) 7 miles Answer: A Diff: 3 Var: 1 Section: 4.5 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

121

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.6

Rectilinear Motion

1) The graph represents a position function. Determine what is happening to the velocity at

A) It is positive.

B) It is negative.

C) It is zero.

D) There is insufficient information to tell.

E) It is +∞.

Answer: C Diff: 1 Var: 1 Section: 4.6

122

2) The graph represents a position function. Determine what is happening to the velocity at

A) It is positive.

B) It is negative.

C) It is zero.

D) There is insufficient information to tell.

E) It is +∞.

Answer: A Diff: 1 Var: 1 Section: 4.6 3) The graph represents a velocity function. The acceleration at t = 5 is

A) negative.

B) positive.

C) zero.

D) There is insufficient information to tell.

E) It is +∞.

Answer: B Diff: 1 Var: 1 Section: 4.6

123

4) Let s(t) = sin 4t be a position function of a particle. At t =

the particle's velocity is

A) Positive B) Negative C) Zero Answer: A Diff: 2 Var: 1 Section: 4.6 5) Let s(t) = − t be a position function of a particle. At -5 the particle's acceleration is A) negative B) positive C) zero Answer: B Diff: 2 Var: 1 Section: 4.6 6) s(t) = 3t − 5 , t ≥ 0. The velocity function is A) 3 - 5t B) 3t - 10 C) 3 - 10t D) 6 - 10t E) 3t - 5t Answer: C Diff: 1 Var: 1 Section: 4.6 7) s(t) = 3t − 4 , t ≥ 0. The acceleration function is A) 3 - 8t B) 8t C) 3 - 8 D) 24t E) 3t - 4t Answer: D Diff: 1 Var: 1 Section: 4.6

124

8) A projectile is dropped, and reaches the ground at 110 m/s. How long does it take the projectile to reach ground? (Assume the position function is A) 5.5 s B) 22 s C) 4.47 s D) 11 s E) 3.16 s Answer: D Diff: 3 Var: 1 Section: 4.6 9) s(t) = 3 − 4. Find t when a = 0.

A) 60 B) -60 C) 3 D) - 3 E) 0 Answer: E Diff: 2 Var: 1 Section: 4.6 10) s(t) = 2 - 5, t ≥ 0. Find s when a = 0.

A) 24 B) -24 C) 5 D) -5 E) 0 Answer: D Diff: 2 Var: 1 Section: 4.6 11) Let s(t) = 3 - 2t be a position function. Find v when A) 3840 B) 1279 C) 3838 D) 3064 E) 2 Answer: C Diff: 2 Var: 1 Section: 4.6

125

where

12) Let s(t) = - 8t + 12 be a position function. The acceleration function a(t) = A) 6 - 8 B) 30 C) 6 - 8t D) 30 - 8 E) 30 Answer: B Diff: 3 Var: 1 Section: 4.6 13) Let s(t) = 2 . Find t when a = 0.

A) 5 B) 40 C) 0 D) 10 E) 1 Answer: C Diff: 3 Var: 1 Section: 4.6

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

126

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.7

Newton's Method

1) Approximate by applying Newton's Method to the equation initial value and calculate three iterations.

A) 3.1622777 B) 3.1621577 C) 3.1622657 D) 3.1622807 E) 3.1666667 Answer: A Diff: 2 Var: 1 Section: 4.7

- 10 = 0. Use 3 for your

2) Approximate by applying Newton's Method to the equation initial value and calculate four iterations.

A) 2 B) 1.9166667 C) 1.9129385 D) 1.9129310 E) 1.9129312 Answer: E Diff: 2 Var: 1 Section: 4.7

Use 2 for your

3) Use Newton's Method to approximate the solutions of and calculate four iterations.

A) -1.8215721, 1.8215721 B) -1.8211604, 1.8211604 C) -1.8211603, 1.8211603 D) -1.8437500, 1.8437500 E) -2, 2 Answer: C Diff: 2 Var: 1 Section: 4.7

127

- 11 = 0. Use 2 for your initial value

4) Use Newton's Method to find the largest positive solution of initial value and calculate eight iterations.

A) 3.1919643 B) 2.4234239 C) 2.6940868 D) 2.4708791 E) 2.4252091 Answer: B Diff: 2 Var: 1 Section: 4.7

-4

5) Use Newton's Method to find the largest positive solution of for your initial value and calculate eight iterations.

A) 2.1591458 B) 2.1517934 C) 2.2455612 D) 2.5384677 E) 3.1085526 Answer: B Diff: 2 Var: 1 Section: 4.7

- 11 = 0. Use 4 for your

Use 4

6) Use Newton's Method to find the largest positive solution of initial value and calculate eight iterations.

A) 2.4155207 B) 2.6478300 C) 2.3540139 D) 3.1289390 E) 3.8955556 Answer: C Diff: 2 Var: 1 Section: 4.7

-5

- 3 = 0. Use 5 for your

7) Use Newton's Method to find the largest positive solution of your initial value and calculate eight iterations.

A) 3.0370370 B) 2.5326278 C) 2.3423456 D) 2.2894319 E) 2.2978693 Answer: D Diff: 2 Var: 1 Section: 4.7

+

- 2x - 7 = 5. Use 4 for

128

8) Use Newton's Method to find the largest positive solution of initial value and calculate eight iterations.

A) 1.4098432 B) 1.4730353 C) 1.7300721 D) 2.2367767 E) 2.9846743 Answer: A Diff: 2 Var: 1 Section: 4.7

Use 4 for your

9) Use Newton's Method to find the largest positive solution of your initial value and calculate eight iterations.

A) 1.8196088 B) 1.9578011 C) 1.8023384 D) 2.3418017 E) 3.0132890 Answer: C Diff: 2 Var: 1 Section: 4.7

Use 4 for

10) Use Newton's Method to find the largest positive solution of for your initial value and calculate three iterations.

A) 2.4357298 B) 2.0465282 C) 1.8340225 D) 1.8339005 E) 1.8340105 Answer: C Diff: 2 Var: 1 Section: 4.7

Use 3

11) Use Newton's Method to find the largest positive solution of for your initial value and calculate eight iterations.

A) 3.1021898 B) 2.5120623 C) 2.0714884 D) 2.1910077 E) 2.0834374 Answer: C Diff: 2 Var: 1 Section: 4.7

Use 4

129

12) Use Newton's Method to find the x-coordinate of the intersection of

and

Use 3 for your initial value and calculate eight iterations.

A) 2.5371901 B) 2.3504285 C) 2.3197631 D) 2.3189842 E) 2.3189837 Answer: E Diff: 3 Var: 1 Section: 4.7 13) Use Newton's Method to approximate the greatest x-coordinate of the intersection of and Use 3 for your initial value and calculate eight iterations.

A) 0.5537293 B) 0.7093985 C) 0.5523116 D) 1.3339736 E) 2.1195652 Answer: C Diff: 3 Var: 1 Section: 4.7 14) Use Newton's Method to find the greatest x-coordinate of the intersection of and A) 2.5870442 B) 2.8836325 C) 2.1058884 D) 4.0562407 E) 3.2053193 Answer: B Diff: 3 Var: 1 Section: 4.7

Use 9 for your initial value and calculate eight iterations.

130

15) Use Newton's Method to find the largest solution of for your initial value and calculate six iterations.

A) -1.2857143 B) -0.9103559 C) -0.6524371 D) -0.5027531 E) -0.5275220 Answer: D Diff: 2 Var: 1 Section: 4.7

Use 2

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

131

Calculus Early Transcendentals, 12e (Anton) Chapter 4 The Derivative in Graphing and Applications 4.8

Rolle's Theorem; Mean-Value Theorem

1) Find the value c such that the conclusion of Rolle's Theorem are satisfied for A) 0 B) -1 C) 1 D) 0.5 E) -0.5 Answer: A Diff: 2 Var: 1 Section: 4.8 2) If f (x) = on [0, 8], find the value c that satisfies the Mean-Value Theorem. (Round to three decimal places.)

A) 1.333 B) 1.540 C) 0.759 D) 1.923 E) 0.385 Answer: B Diff: 2 Var: 1 Section: 4.8 3) Find the value for which f (x) = A) 3.5 B) 4 C) 4.5 D) 3.66 E) 2.33 Answer: B Diff: 2 Var: 1 Section: 4.8

+ 9 on [3, 5] satisfies the Mean-Value Theorem.

4) Find the value for which f (x) = A) 2.517 B) 1.915 C) 4.583 D) 2.646 E) 3.240 Answer: D Diff: 2 Var: 1 Section: 4.8

− 7 on [1, 4] satisfies the Mean-Value Theorem.

132

on

5) Find the value c that satisfies Rolle's Theorem for f (x) = cos 2x on A) B) 2π C) 0 D) E) Answer: D Diff: 2 Var: 1 Section: 4.8 6) Find the value c that satisfies the Mean-Value Theorem for f (x) =

on

A) B) C) 4 D) 0 E) Answer: A Diff: 2 Var: 1 Section: 4.8 7) Find the value c that satisfies Rolle's Theorem for f (x) = A) -2.0 B) 1.2 C) 2.0 D) 4.0 E) -4.0 Answer: B Diff: 2 Var: 1 Section: 4.8

133

- 4x on [-2, 2].

8) Find the value c that satisfies Rolle's Theorem for f (x) = 6 cos 5x on

.

A) B) C) 0 D) E) Answer: C Diff: 2 Var: 1 Section: 4.8

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134

Calculus Early Transcendentals, 12e (Anton) Chapter 5 Integration 5.1

An Overview of the Area Problem

1) Given f (x) = 3x. Use the rectangle method to approximate the area on the range 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A) 16.875 B) 10.125 C) 13.5 D) 20.25 E) 6.75 Answer: C Diff: 1 Var: 1 Section: 5.1

using

2) Given f (x) = 2 + x. Use the rectangle method to approximate the area on the interval using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A) 25.625 B) 19.375 C) 28.75 D) 11.25 E) 22.5 Answer: E Diff: 1 Var: 1 Section: 5.1 3) Given f (x) = + 4. Use the rectangle method to approximate the area on the range [0, 6] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A) 38.547 B) 39.464 C) 37.562 D) 40.348 E) 19.348 Answer: A Diff: 2 Var: 1 Section: 5.1

135

4) Given f (x) = 4x - 1, [0.5, 2.5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A) 12 B) 10 C) 8 D) 14 E) 5 Answer: B Diff: 1 Var: 1 Section: 5.1 5) Given f (x) = , [3, 3]. Use the rectangle method to approximate the area using 4 rectangles.

(Assume the graph goes through the midpoint of each rectangle.)

A) 3.845162 B) 3.898262 C) 3.787961 D) 3.949357 E) 3.728753 Answer: A Diff: 2 Var: 1 Section: 5.1 6) Given f (x) = + 8, [3, 5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A) 4841.000000 B) 19,737.000000 C) 14,947.515625 D) 7499.515625 E) 10,685.053223 Answer: E Diff: 2 Var: 1 Section: 5.1 7) Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function and the interval A) 3(x - 5) B) 3(x + 5) C) 3x D) 15 E) 3 Answer: A Diff: 2 Var: 1 Section: 5.1

136

8) Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function and the interval A)

(5x + 3)(x - 5)

B)

(5x + 3)(x + 5)

C)

(5x + 53)(x + 5)

D) -5.5(x + 5) E)

(5x + 3)

Answer: B Diff: 3 Var: 1 Section: 5.1 9) Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function and the interval A)

(5x - 27)(x - 1)

B)

(5x - 27)(x + 1)

C)

(5x - 16)(x + 1)

D) 3(x + 1) E)

(5x + 27)(x + 1)

Answer: B Diff: 3 Var: 1 Section: 5.1

137

10) Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f (x) = 10x + 11 and the interval [a, x] = [0, x].

A) 5 - 11x B) 5x + 11 C) 5 + 22x D) 10 + 11x E) 5 + 11x Answer: E Diff: 1 Var: 1 Section: 5.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

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138

Calculus Early Transcendentals, 12e (Anton) Chapter 5 Integration 5.2

The Indefinite Integral

1) Which of the following expressions is an antiderivative of the function f (x) = -2 A) -2 + C B) -6 + C C) -

on

+C

D) -4x + C E) -2x + C Answer: C Diff: 1 Var: 1 Section: 5.2 2) Which of the following expressions is an antiderivative of the function f (x) = 2 A)

+

+5

B)

+2

+5

C) 10

+ 32

+5

D)

+

+5

E)

+

+ 5x

Answer: A Diff: 1 Var: 1 Section: 5.2 3) Evaluate: A) 8 B) 8x + C C) 8 + C D) 4 + C E) 9 + C Answer: D Diff: 2 Var: 1 Section: 5.2 139

+8

on

4) Given f (x) = 7 A)

+ 2, which of the following is equal to

?

+ 2x + C

B) 7 + 2 C) 28 + 2 D) 7 + 2 E) 7 + 2x + C Answer: D Diff: 1 Var: 1 Section: 5.2 5) Given

= 3x + 2 and y(4) = 34, which of the following is equal to y?

A) 3x + 4 B)

+ 2x + 2

C)

+ 2x + 4

D)

+ 4x

E) 14 Answer: B Diff: 1 Var: 1 Section: 5.2 6) The velocity of a falling object is given by the integral

, where 9.81 m/

is the

acceleration due to gravity on the surface of the earth and the negative sign indicates downward motion. If an object has an initial downward velocity of 7 m/s, what is the expression for its velocity at a given time t ≥ 0?

A) v(t) = -9.81t + 7 B) v(t) = -9.81t - 7 C) v(t) = -9.81t D) v(t) = -9.81 - 7 E) v(t) = -9.81 + 7 Answer: B Diff: 1 Var: 1 Section: 5.2

140

7) A curve in the xy-plane has the property that at each point (x, y) on the curve, the tangent line has a slope of 6 . Which function describes the curve if the curve passes through the point A)

-3

B)

- 3x

C) 24

-3

D)

-3

E)

+3

Answer: A Diff: 3 Var: 1 Section: 5.2 8) Given

[h(x)] = 3 cos x − 4 sin x, what is ℎ(x)?

A) 3sin x + 4cos x + C B) -3sin x + 4cos x + C C) 3sin x - 4cos x + C D) -3sin x - 4cos x + C E) 24sin x cos x + C Answer: A Diff: 3 Var: 1 Section: 5.2 9) Given A) 2

[ f (x)] = 2

- 10x, what is f (x)?

- 10

B) 2 + 5x + C C) 2 - 10 + C D) 2 - 5 + C E) 2 + 5 + C Answer: D Diff: 3 Var: 1 Section: 5.2

141

10) Given

[ f (x)] =

A) 9ln(36 +

)+C

B)

tan

C)

, find f (x).

+C +C

D) 18x + 6 E)

+C

Answer: E Diff: 3 Var: 1 Section: 5.2 11) Given

[ f (x)] =

A) 5ln(49 +

)+C

B)

+C

C) 5

+C

, find f (x).

D) 10x + 7 E)

+C

Answer: C Diff: 3 Var: 1 Section: 5.2

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

142

Calculus Early Transcendentals, 12e (Anton) Chapter 5 Integration 5.3

Integration by Substitution

1)

=

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: A Diff: 1 Var: 1 Section: 5.3 2)

=

A) -

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: E Diff: 2 Var: 1 Section: 5.3

143

3)

=

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: B Diff: 2 Var: 1 Section: 5.3 4) A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: C Diff: 1 Var: 1 Section: 5.3

144

5) A) ln

= +C

B)

+C

C)

+C

D) ln

+C

E) +C Answer: C Diff: 3 Var: 1 Section: 5.3 6)

=

A)

+C

B)

+C

C)

+C

D) 8

+C

E)

+C

Answer: C Diff: 1 Var: 1 Section: 5.3

145

7)

= A)

sin

B)

cos

C) 3 cos D) 3 sin E)

cos

Answer: B Diff: 3 Var: 1 Section: 5.3 8) For

what is a good choice for u?

A) B) sin x C) D) sin E) Answer: A Diff: 1 Var: 1 Section: 5.3

146

9) For A) B)

what would be a good choice for u? +3

C) D) E) Answer: A Diff: 2 Var: 1 Section: 5.3 10) Evaluate A)

.

tan 5x + C

B) tan 5x + C C) -

tan 5x + C

D) - tan 5x + C E) cot 5x + C Answer: A Diff: 2 Var: 1 Section: 5.3 11) Evaluate A) B)

.

x+C x+C

C)

x+C

D)

x+C

E) x+C Answer: A Diff: 2 Var: 1 Section: 5.3

147

12) Evaluate A) 5 sin B) sin

.

+C +C

C) 4 cos

+C

D) -4 cos

+C

E) 5 cos +C Answer: A Diff: 3 Var: 1 Section: 5.3 13) Evaluate

.

A) -

+C

B)

+C

C) -

+C

D)

+C

E)

+C

Answer: A Diff: 2 Var: 1 Section: 5.3

148

14) Evaluate

A)

.

+C

B)

+C

C) -

+C

D) -

+C

E)

+C

Answer: A Diff: 2 Var: 1 Section: 5.3 15) Evaluate the integral by making the indicated substitution.

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

,

Answer: A Diff: 2 Var: 1 Section: 5.3 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 149

Chapter 5 5.4 1)

Integration

The Definition of Area as a Limit; Sigma Notation =

A) 4368 B) 1456 C) 91 D) 728 E) 168 Answer: D Diff: 1 Var: 1 Section: 5.4 2)

=

A) 28,975 B) 19,500 C) 97,500 D) 94,500 E) 97,625 Answer: E Diff: 2 Var: 1 Section: 5.4 3)

=

A) 4 B) 0 C) 8 D) 5 E) 3 Answer: B Diff: 2 Var: 1 Section: 5.4

150

4) Express in sigma notation, but do not evaluate. 5 + 6 + 7 + 8 A)

B)

C)

D)

E) Answer: B Diff: 2 Var: 1 Section: 5.4 5) Express in sigma notation, but do not evaluate. 16 + 25 + 36 + 49 + 64 + 81 + 100 A)

B)

C)

D)

E) Answer: C Diff: 2 Var: 1 Section: 5.4

151

6)

=

A) 2448 B) 18 C) 1632 D) 1224 E) 324 Answer: A Diff: 2 Var: 1 Section: 5.4 7)

=

A) B) C) 1 D) E) 0 Answer: D Diff: 3 Var: 1 Section: 5.4 8)

=

A) 9 B) 8 C) 72 D) E) Answer: B Diff: 3 Var: 1 Section: 5.4

152

9) Express

+

+

+

in sigma notation.

A)

B)

C)

D) E) None of these Answer: A Diff: 2 Var: 1 Section: 5.4 10) Write the expression in sigma notation. 4 - 8 + 12 - 16 + 20 - 24 + 28.

A)

B)

C) -4

D) 4 E) None of these Answer: A Diff: 3 Var: 1 Section: 5.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 153

Chapter 6 6.1

Applications of the Definite Integral in Geometry, Science, and Engineering

Area Between Two Curves

1) Find the area of the region enclosed by the curves y = 5 to x. Approximate area to three decimal places.

A) 2.5 B) 0.833 C) 10.417 D) 29.167 E) 4.167 Answer: B Diff: 1 Var: 1 Section: 6.1 2) Find the area enclosed by the curves y = decimal places.

A) 0.295 B) 0.300 C) 0.292 D) 0.395 E) 2.379 Answer: A Diff: 1 Var: 1 Section: 6.1

,y=

and y = 5x by integrating with respect

, x = 0, x = 0.5. Approximate area to three

3) Find the area enclosed by the curves y = sin 4x, y = 3x + 3, x = 0, x = 3π. Approximate area to three decimal places.

A) 78.734 B) 59.218 C) 74.926 D) 78.067 E) 9.870 Answer: D Diff: 3 Var: 1 Section: 6.1

154

4) Find the area between the curves y =

,y=

+ 2. Approximate area to three decimal

places.

A) 9.000 B) 30.000 C) 12.000 D) 16.000 E) 7.000 Answer: C Diff: 2 Var: 1 Section: 6.1 5) Find the area between the curves x = places.

A) 12 B) 9 C) 10 D) 13 E) 0 Answer: B Diff: 2 Var: 1 Section: 6.1

, x = -y + 11, y = 0. Approximate area to three decimal

6) Use a graphing utility to find the area of the region enclosed by the curves Approximate area to three decimal places.

A) 76.500 B) 38.250 C) 56.250 D) 9.750 E) 15.750 Answer: E Diff: 3 Var: 1 Section: 6.1 7) Use a graphing utility to find the area enclosed by the curves Approximate area to three decimal places.

A) 0.367 B) 0.033 C) 0.450 D) 0.050 E) 2.000 Answer: A Diff: 2 Var: 1 Section: 6.1 155

8) Use a graphing utility to find the region enclosed by the curves x = to three decimal places.

A) 1.050 B) 1.133 C) 0.467 D) 0.550 E) 0.750 Answer: D Diff: 3 Var: 1 Section: 6.1 9) Find a vertical line x = k that divides the area enclosed by y = parts. Approximate area to three decimal places.

A) 3 B) 3.780 C) 12 D) 4.243 E) 9.524 Answer: B Diff: 3 Var: 1 Section: 6.1

,x=

,

and

10) Approximate the area of the region that lies below y = cos x and above Approximate area to three decimal places.

A) 0.8679 B) 0.852 C) 1 D) 0.785 E) 0.8821 Answer: A Diff: 3 Var: 1 Section: 6.1 11) Use a graphing utility to find the area enclosed by the curves y = Approximate area to two decimal places.

A) 992 B) 56 C) 936 D) 162.66 E) 1 Answer: C Diff: 2 Var: 1 Section: 6.1

156

. Approximate area

into equal

where

, y = x, x = 4, and x = 8.

12) Use a graphing utility to find the area enclosed by the curves x = Approximate area to two decimal places.

A) 992 B) 56 C) 936 D) 162.66 E) 1 Answer: C Diff: 2 Var: 1 Section: 6.1

, x = y,

and

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

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157

Calculus Early Transcendentals, 12e (Anton) Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering 6.2

Volumes by Slicing; Disks and Washers

1) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves decimal places.

A) 6870.663 B) 381.704 C) 63.617 D) 981.523 E) 28.274 Answer: D Diff: 1 Var: 1 Section: 6.2

about the x-axis. Approximate area to three

2) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves

about the x-axis.

A) π B) C) 8π D) E) Answer: B Diff: 3 Var: 1 Section: 6.2 3) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves three decimal places.

A) 111.072 B) 78.540 C) 11.806 D) 236.954 E) 90.346 Answer: E Diff: 2 Var: 1 Section: 6.2

about the x-axis. Approximate area to

158

4) Find the value of the solid that is obtained when the region under the curve y = interval is revolved about the x-axis.

over the

A) B) 261,632π C) D) 9π E) Answer: A Diff: 1 Var: 1 Section: 6.2 5) Which integral gives the volume of the solid that results when the region enclosed by the curves and

is revolved about the x-axis?

A)

B)

C)

D)

E) Answer: A Diff: 1 Var: 1 Section: 6.2

159

6) Which integral gives the volume of the solid that results when the region enclosed by the curves and is revolved about the x-axis?

A)

B)

C)

D)

E) Answer: B Diff: 1 Var: 1 Section: 6.2

160

7) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves three decimal places.

A) 39.986 B) 28.274 C) 4.250 D) 85.303 E) 32.524 Answer: E Diff: 2 Var: 1 Section: 6.2

about the y-axis. Approximate area to

8) Find the value of the solid that is obtained when the region enclosed by the curves is revolved about the y-axis.

A) B) 16,256π C) D) 7π E) Answer: A Diff: 1 Var: 1 Section: 6.2 9) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves decimal places.

A) 21.991 B) 37.699 C) 6.283 D) 16.283 E) 8.312 Answer: B Diff: 3 Var: 1 Section: 6.2

about the y-axis. Approximate area to three

161

10) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves x = , x = y + 20, about the y-axis. Approximate area to three decimal places.

A) 2452.956 B) 6021.386 C) 3730.641 D) 5008.327 E) 1256.637 Answer: B Diff: 2 Var: 1 Section: 6.2 11) Find the volume of the hemisphere created by rotating the area enclosed by the circle and above

around the y-axis. Approximate area to three decimal places.

A) 18.000 B) 70.686 C) 56.549 D) 113.097 E) 13.329 Answer: C Diff: 2 Var: 1 Section: 6.2 12) Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y =

x, x = 0, x =

about the x-axis. Approximate area to three

decimal places.

A) 3.553 B) 0.820 C) 0.355 D) 0.243 E) 0.972 Answer: B Diff: 3 Var: 1 Section: 6.2

162

13) Find the value of the solid that is obtained when the region under the curve over the interval is revolved about the x-axis. Approximate area to three decimal places.

A) 4921.905 B) 148.952 C) 4772.952 D) 14,994.672 E) 15,462.620 Answer: D Diff: 2 Var: 1 Section: 6.2 14) Find the volume of the solid that results when the area of the region enclosed by 5x + 3y = 15, y = 0, x = 0 is revolved about the y-axis.

A) 5π B) 15π C) 30π D) 60π E) 120π Answer: A Diff: 1 Var: 1 Section: 6.2 15) Use the method of disks to find the volume of the solid that results when the area of the region enclosed by

and

is revolved about the x axis.

π

A) B)

π

C)

π

D)

π

E)

π

Answer: A Diff: 2 Var: 1 Section: 6.2

163

16) Use the method of washers to find the volume of the solid that results when the area enclosed by and A) 48π B) 72π C) 36π D) 24π E) 18π Answer: A Diff: 2 Var: 1 Section: 6.2

is revolved about the x-axis.

17) Use the method of washers to find the volume of the solid that results when the area of the region enclosed by A)

and

is revolved about the x-axis.

π

B)

π

C)

π

D)

π

E) 18π Answer: A Diff: 2 Var: 1 Section: 6.2 18) Use the method of washers to find the volume of the solid that results when the area of the region enclosed by and is revolved about A)

π

B)

π

C) 320π D)

π

E) 640π Answer: A Diff: 3 Var: 1 Section: 6.2

164

19) A pyramid is 38 feet high. The cross sections are all squares and the base is a square of side 21 feet. Find the volume of the pyramid.

A) 1862 B) 3724 C) 5586 D) 7448 E) 11,172 Answer: A Diff: 3 Var: 1 Section: 6.2

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165

Calculus Early Transcendentals, 12e (Anton) Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering 6.3

Volumes by Cylindrical Shells

1) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 609π B) C) D) E) Answer: D Diff: 1 Var: 1 Section: 6.3 2) Use cylindrical shells to find the volume of the solid when the region enclosed by between and is revolved about the y-axis.

A) 31π B) 24.8π C) 12.4π D) 5.6π E) 41.333π Answer: B Diff: 2 Var: 1 Section: 6.3 3) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 0.511π B) 1.022π C) 3.199π D) 5.416π E) 2.708π Answer: B Diff: 2 Var: 1 Section: 6.3 166

and

4) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 0.016π B) 0.500π C) 0.494π D) 0.247π E) 0.398π Answer: C Diff: 3 Var: 1 Section: 6.3 5) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 0.353π B) 0.547π C) 0.647π D) 0.454π E) 0.546π Answer: C Diff: 3 Var: 1 Section: 6.3 6) Use cylindrical shells to find the volume of the solid generated when the region R under over the interval is revolved about the x-axis.

A) B) C) 6561π D) E) Answer: B Diff: 2 Var: 1 Section: 6.3

167

7) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 378π B) C) D) 108π E) 54π Answer: E Diff: 3 Var: 1 Section: 6.3 8) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) B) 128π C) D) 3π E) Answer: A Diff: 2 Var: 1 Section: 6.3 9) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the x-axis.

A) 13.5π B) 40.5 C) 81π D) 40.5π E) π Answer: D Diff: 1 Var: 1 Section: 6.3

168

10) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the x-axis.

A) B) C) 64π D) E) Answer: D Diff: 2 Var: 1 Section: 6.3 11) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the x-axis.

A) 69.333π B) 0.01π C) 1.333π D) π E) 2.667π Answer: E Diff: 3 Var: 1 Section: 6.3 12) Use cylindrical shells to find the volume of the solid when the region enclosed by is revolved about the y-axis.

A) 2.666π B) 0.01π C) 1.333π D) π E) 2.667π Answer: E Diff: 3 Var: 1 Section: 6.3

169

13) Use cylindrical shells to find the volume of the solid when the region enclosed by y = x2, x = 3, is revolved about the line A) 22.500π B) 11.250π C) 456.000π D) 5.625π E) 2.011π Answer: A Diff: 3 Var: 1 Section: 6.3 14) Answer true or false. The region enclosed by revolving the semicircle y = about the x-axis is

.

Answer: TRUE Diff: 2 Var: 1 Section: 6.3 15) Use cylindrical shells to find the volume of the solid generated when the region R under over the interval is revolved about the x-axis.

A) 49π B) C) D) E) Answer: B Diff: 2 Var: 1 Section: 6.3

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170

Calculus Early Transcendentals, 12e (Anton) Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering 6.4

Length of a Plane Curve

1) Find the arc length of the curve y = 2 places.

A) 6.06π B) 81.82 C) 81.82π D) 6.13 E) 6.06 Answer: E Diff: 1 Var: 1 Section: 6.4 2) Find the arc length of the curve y =

from x = 0 to x = 2. Approximate area to two decimal

from x = 0 to x = 2.

A) 7.783 B) 18.739 C) 7.169 D) 17.436 E) 6.495 Answer: A Diff: 2 Var: 1 Section: 6.4 3) The arc length of the curve x =

from y = 0 to y = 1 is

A) 3.491 B) 1.197 C) 1.132 D) 3.166 E) 1.165 Answer: B Diff: 3 Var: 1 Section: 6.4

171

4) Approximate the arc length of y = sin x from x = 0 to x =

.

A) 2.109 B) 1.709 C) 2.109π D) 1.909 E) 1.909π Answer: D Diff: 2 Var: 1 Section: 6.4 5) Approximate the arc length of x = sin 4y from y = 0 to y = π.

A) 4.406 B) 8.812 C) 17.624 D) 8.832 E) 8.712 Answer: B Diff: 2 Var: 1 Section: 6.4 6) Approximate the arc length of y = sin 4x from x = 0 to x = π.

A) 4.406 B) 8.812 C) 17.624 D) 8.832 E) 8.712 Answer: B Diff: 2 Var: 1 Section: 6.4 7) Approximate the arc length of y = cos x + 4 sin x from x = 0 to x = π.

A) 81.740 B) 9.041 C) 18.082 D) 4.521 E) 8.841 Answer: B Diff: 3 Var: 1 Section: 6.4 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

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172

Calculus Early Transcendentals, 12e (Anton) Chapter 7 Principles of Integral Evaluation 7.1

An Overview of Integration Methods

1) Evaluate

dx.

A)

+C

B) -

+C

C) -

+C

D)

+C

E) -

+C

Answer: C Diff: 1 Var: 1 Section: 7.1 2) Evaluate

dx.

A) -

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: C Diff: 1 Var: 1 Section: 7.1

173

3) Evaluate

dx.

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: D Diff: 2 Var: 1 Section: 7.1 4) Evaluate A)

+C

B)

+C

C)

+C

D) 5

+C

E)

+C

dx.

Answer: A Diff: 2 Var: 1 Section: 7.1 5)

dx =

A) +C B) +C C) cos +C D) +C E) sin +C Answer: B Diff: 2 Var: 1 174

Section: 7.1 6)

dx =

A)

+C

B)

+C

C)

+C

D)

+C

E) -

+C

Answer: B Diff: 2 Var: 1 Section: 7.1

7)

dx =

A)

+C

B) 5

+C

C) -

+C

D)

+C

E) 25 +C Answer: D Diff: 3 Var: 1 Section: 7.1

175

8)

dx =

A)

+C

B)

+C

C) ln

+C

D)

+C

E)

+C

Answer: C Diff: 3 Var: 1 Section: 7.1 9)

=

A) ln

+C

B) -

ln

+C

C)

ln

+C

D) -

ln

+C

E) -ln +C Answer: B Diff: 3 Var: 1 Section: 7.1

176

10)

=

A)

+C

B)

+C

C)

+C

D)

+C

E) 4 x+C Answer: A Diff: 2 Var: 1 Section: 7.1 11)

=

A)

+

+C

B)

+

+C

C)

-

+C

D) E)

+

+C +C

Answer: B Diff: 1 Var: 1 Section: 7.1

177

12)

dx =

A) -ln

+C

B) ln

+C

C) ln

+C

D) 7 +C E) 7 + +C Answer: B Diff: 3 Var: 1 Section: 7.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

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178

Calculus Early Transcendentals, 12e (Anton) Chapter 7 Principles of Integral Evaluation 7.2

Integration by Parts

1)

=

A)

(2x - 1) + C

B)

(2x - 1) + C

C)

+C

D)

+C

E) 2 +C Answer: B Diff: 2 Var: 1 Section: 7.2 2)

=

A)

(64

B)

+C

C)

+C

D) 8

+C

- 16x + 2) + C

E) 64 +C Answer: A Diff: 3 Var: 1 Section: 7.2

179

3)

=

A)

+C

B)

+C

C)

+

+C

D)

+

+C

E) sin 6x + C Answer: C Diff: 2 Var: 1 Section: 7.2 4)

=

A)

-

+C

B)

+

+C

C) D) E) -

-

+C

-

+C +C

Answer: A Diff: 1 Var: 1 Section: 7.2

180

5)

=

A)

+

+

+C

B)

-

-

+C

C)

+

-

+C

D) 2 cos 3x +

-

E) 2 cos 3x -

-

+C +C

Answer: C Diff: 3 Var: 1 Section: 7.2 6)

=

A)

+

+C

B)

-

+C

C) 3 ln(6x) - 3 + C D) ln(6x) +C E)

-

+C

Answer: B Diff: 2 Var: 1 Section: 7.2

181

7)

=

A) x

(2x) +

+C

B) x

(2x) -

+C

C) x

(2x) + C

D) x

(2x) +

+C

E) x

(2x) +

+C

Answer: E Diff: 3 Var: 1 Section: 7.2 8)

=

A)

(2 sin 6x - 6 cos 6x) + C

B) C)

(2 sin 6x - 6 cos 6x) + C (2 sin 6x + 6 cos 6x) + C

D)

(2 sin 6x - 6 cos 6x) + C

E)

(2 sin 6x - 6 cos 6x) + C

Answer: D Diff: 2 Var: 1 Section: 7.2 9)

=

A) 5.54 B) 2.10 C) 0.13 D) 0.00 E) 7.39 Answer: B Diff: 2 Var: 1 Section: 7.2 182

10)

=

A) 1.07 B) 0.85 C) -1.95 D) 1.85 E) 1.00 Answer: A Diff: 2 Var: 1 Section: 7.2 11)

=

A) 3.74 B) 0.92 C) -0.24 D) -0.06 E) -1.73 Answer: B Diff: 3 Var: 1 Section: 7.2

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photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) Chapter 7 Principles of Integral Evaluation 7.3

Integrating Trigonometric Functions

1)

=

A)

+C

B)

+C

C)

+C

D)

x+C

E) -

+C

Answer: B Diff: 1 Var: 1 Section: 7.3 2)

=

A)

-

+C

B)

-

+C

C)

-

+C

D)

-

+C

E)

+

+C

Answer: A Diff: 1 Var: 1 Section: 7.3

184

3)

=

A)

(3x) +

cos(3x) + C

B)

cos(3x) + C

C)

(3x) -

cos(3x) + C

D)

(3x) -

sin(3x) + C

E)

(3x) -

cos(3x) + C

Answer: E Diff: 1 Var: 1 Section: 7.3 4)

=

A)

sin(8x) +

(8x) + C

B)

cos(8x) -

(8x) + C

C)

sin(8x) -

(8x) + C

D)

sin(8x) -

(8x) + C

E)

cos(8x) +

(8x) + C

Answer: C Diff: 1 Var: 1 Section: 7.3

185

5)

=

A)

x+

sin(4x) -

sin(8x) + C

B)

x+

sin(4x) +

sin(8x) + C

C)

x+

sin(4x) +

sin(8x) + C

D)

x+

sin(4x) +

sin(8x) + C

E)

x+

sin(8x) + C

Answer: D Diff: 2 Var: 1 Section: 7.3 6)

=

A)

-

+C

B)

+

+C

C)

-

+C

D)

+

+C

E)

-

+C

Answer: A Diff: 2 Var: 1 Section: 7.3

186

7)

=

A)

+C

B)

+C

C)

+C

D)

+C

E) -ln +C Answer: B Diff: 2 Var: 1 Section: 7.3 8) Evaluate the following integral: A) -

cos(9x) -

cos(3x) + C

B) -

cos(9x) +

sin(3x) + C

C)

cos(9x) +

cos(3x) + C

D)

sin(9x) +

sin(3x) + C

E) -

sin(9x) +

cos(3x) + C

Answer: A Diff: 2 Var: 1 Section: 7.3

187

9)

=

A) -

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: D Diff: 1 Var: 1 Section: 7.3 10)

=

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: E Diff: 2 Var: 1 Section: 7.3

188

11) Evaluate the following integral: A)

x+C

B)

x+C

C) D) E) -

x+C sec x

x+C

x+C

Answer: B Diff: 1 Var: 1 Section: 7.3 12)

=

A)

+C

B)

+C

C) (2x) + C D) (2x) + C E) (2x) + C Answer: A Diff: 2 Var: 1 Section: 7.3

189

13)

=

A)

(6x) + C

B)

+C

C) 6 (6x) + C D) 36 (6x) + C E) (6x) + C Answer: A Diff: 1 Var: 1 Section: 7.3 14) Evaluate the integral: A) -

(7x) +

(7x) + C

B)

(7x) -

(7x) + C

C)

(7x) -

(7x) + C

D) -

(7x) +

(7x) + C

E)

(7x) +

(7x) + C

Answer: B Diff: 1 Var: 1 Section: 7.3

190

15) Evaluate the integral: A) -

(4x) +

(4x) + C

B)

(4x) -

(4x) + C

C)

(4x) -

(4x) + C

D) -

(4x) +

(4x) + C

E)

(4x) +

(4x) + C

Answer: A Diff: 2 Var: 1 Section: 7.3 16) Evaluate the integral: A)

(2x) +

(2x) + C

B)

(2x) -

(2x) + C

C)

(2x) +

(2x) + C

D) -

(2x) -

(2x) + C

E)

(2x) -

(2x) + C

Answer: C Diff: 2 Var: 1 Section: 7.3

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

191

Calculus Early Transcendentals, 12e (Anton) Chapter 7 Principles of Integral Evaluation 7.4

Trigonometric Substitutions

1)

dx =

A)

-

B)

+

C)

+

+C

D)

+

+C

E)

+C

sin

-

+C

+C

Answer: D Diff: 3 Var: 1 Section: 7.4 2)

dx =

A)

-

B)

+

C)

+

+C

D)

+

+C

E)

-

+C

sin

+C

+C

Answer: D Diff: 3 Var: 1 Section: 7.4 192

193

3)

=

A) ln

+C

B) -ln

+C

C)

+C

D)

+C

E)

+C

Answer: C Diff: 2 Var: 1 Section: 7.4 4)

dx =

(Approximate answer to three decimal places.)

A) 0.548 B) 0.8645 C) -4.430 D) 4.430 E) 1.729 Answer: E Diff: 2 Var: 1 Section: 7.4 5)

=

(Approximate answer to three decimal places.)

A) 0.956 B) 0.025 C) 0.045 D) 0.033 E) 1.901 Answer: B Diff: 2 Var: 1 Section: 7.4

194

6)

=

(Approximate answer to three decimal places.)

=

(Approximate answer to three decimal places.)

A) 0.111 B) 0.030 C) 0.004 D) 0.002 E) 0.061 Answer: D Diff: 2 Var: 1 Section: 7.4 7) A) 0.026 B) 0.419 C) 0.222 D) 0.046 E) 0.012 Answer: A Diff: 3 Var: 1 Section: 7.4 8)

=

(Approximate answer to three decimal places.)

A) 7.993 B) 7.326 C) 7.936 D) 7.805 E) 7.631 Answer: B Diff: 3 Var: 1 Section: 7.4

195

9) A)

+8

+ 4x + C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: D Diff: 3 Var: 1 Section: 7.4

196

10)

A)

+C

B)

+C

C)

+C

D)

+C

E)

+C

Answer: B Diff: 3 Var: 1 Section: 7.4 11)

=

(Approximate answer to three decimal places.)

A) 2.366 B) 0.186 C) 0.889 D) 1.571 E) 0.775 Answer: E Diff: 2 Var: 1 Section: 7.4

197

12)

=

(Approximate answer to three decimal places.)

A) 0.258 B) 0.069 C) 0.119 D) 0.189 E) 0.565 Answer: C Diff: 3 Var: 1 Section: 7.4 13)

=

(Approximate answer to three decimal places.)

A) 0.342367 B) 0.32523 C) 0.469367 D) 0.361367 E) 0.384367 Answer: D Diff: 2 Var: 1 Section: 7.4 14)

=

(Approximate answer to three decimal places.)

A) 1 B) 0 C) -1 D) 6 E) -6 Answer: B Diff: 1 Var: 1 Section: 7.4 15)

=

(Approximate answer to three decimal places.)

A) 0.775 B) 0.795 C) 0.357 D) 2.014 E) 0.611 Answer: A Diff: 2 Var: 1 198

Section: 7.4 16)

=

(Approximate answer to three decimal places.)

A) 2.975 B) 0.992 C) 0.496 D) 1.488 E) 0.823 Answer: B Diff: 2 Var: 1 Section: 7.4 17)

=

(Approximate answer to three decimal places.)

A) 0.652 B) 0.877 C) 36.250 D) 0.392 E) 0.475 Answer: D Diff: 2 Var: 1 Section: 7.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, 199

photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) Chapter 8 Mathematical Modeling with Differential Equations 8.1

Modeling with Differential Equations

1) State the order of the differential equation, and decide which family of functions is a solution.

- 4y = 0 A) y =

; 1st order

B) y = ; 1st order C) y = ; 2nd order D) y = ; 1st order E) y = ; 2nd order Answer: A Diff: 1 Var: 1 Section: 8.1 2) State the order of the differential equation, and decide which family of functions is a solution.

- 8y = -7 A) ; 2nd order B) y = ; 1st order C) y = + ; 1st order D) y = -ln + C; 2nd order E) y = ; 2nd order Answer: C Diff: 1 Var: 1 Section: 8.1

200

3) State the order of the differential equation, and decide which family of functions is a solution.

- 14

+ 49y = 0

A) + B) + C) (A + Bx) +

; 1st order ; 1st order ; 2nd order

D) y =

+ B ; 2nd order

E) y =

+B

; 2nd order

Answer: C Diff: 2 Var: 1 Section: 8.1 4) State the order of the differential equation, and decide which family of functions is a solution. +x

- 81y = 0

A) + B) + C) y = +C

; 2nd order ; 1st order ; 1st order

D) y =

+ B ; 2nd order

E) y =

+B

; 2nd order

Answer: D Diff: 2 Var: 1 Section: 8.1 5) If y = 330 , k > 0, the situation modeled is A) increasing B) decreasing C) remaining constant D) More information is needed.

E) Cannot be determined.

Answer: B Diff: 1 Var: 1 Section: 8.1 201

6) If y = 490 , k > 0, the situation modeled is A) increasing B) decreasing C) remaining constant D) More information is needed.

E) Cannot be determined.

Answer: A Diff: 1 Var: 1 Section: 8.1 7) If

=

, the situation modeled is

A) increasing B) decreasing C) remaining constant D) More information is needed.

E) Cannot be determined.

Answer: A Diff: 1 Var: 1 Section: 8.1 8) Suppose that an initial population of 80 bacteria grows exponentially at a rate of 3% per hour.

How many bacteria are present after t hours?

A) 80t B) 80 C) 80 D) 80 E) 80 Answer: D Diff: 3 Var: 1 Section: 8.1

202

9) Suppose that an initial population of 90 bacteria dies exponentially at a rate of 3% per hour.

How many bacteria are present after t hours?

A) 90t B) 90 C) 90 D) 90 E) 90 Answer: D Diff: 3 Var: 1 Section: 8.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

203

Calculus Early Transcendentals, 12e (Anton) Chapter 8 Mathematical Modeling with Differential Equations 8.2

Separation of Variables

1) What is the solution to the following differential equation? (Use separation of variables!)

-4

=0

A) y = 12

+ 18

+C

B) y = C) y = 18

+C

D) y = -

+C

E) y = -

+ 4C

Answer: B Diff: 1 Var: 1 Section: 8.2 2) What is the solution to the following differential equation? +8

=0

A) y = 24

+ 42

B) y = -

+C

C) y = 42

+C

+C

D) y =

E) y = -

+ 8C

Answer: D Diff: 2 Var: 1 Section: 8.2

204

3) What is the solution to the following differential equation? (Use separation of variables!)

3

=

A) y = 3 + C B) =3 +C C) y = D)

=6

E) y = 3 Answer: B Diff: 1 Var: 1 Section: 8.2 4) What is the solution to the following initial-value problem? (Use separation of variables!) = 7y; y(0) = 2 A) y = 2 B) y = 7 C) y = 7 D) y = E) y = Answer: A Diff: 1 Var: 1 Section: 8.2 5) What is the solution to the following differential equation? = A) y = 3

+C

B) y =

+C

C) y = 27t + C D) y = 54t + C E) y = Answer: E Diff: 2 Var: 1 Section: 8.2 205

6) What is the solution to the following differential equation? = A) y = 2.5

+C

B) y =

+C

C) y = 33t + C D) y = E) y = Answer: D Diff: 2 Var: 1 Section: 8.2 7) What is the solution to the following differential equation? = A) y = 3

+C

B) y =

+C

C) y = D) y = 72t + C E) y = Answer: C Diff: 2 Var: 1 Section: 8.2

206

8) Solve the differential equation by separation of variables. = A) 5

+C

B)

+C

C)

+C

D)

+ 7x + C

E)

- 7x + C

Answer: A Diff: 1 Var: 1 Section: 8.2 9) Find the solution of the IVP (6y - sin y)

=6

implicit question.

A) 3 - cos y = 2 + 6x - 1 B) 3 - cos y = 2 + 6x - 5 C) 3 + cos y = 2 + 6x + 1 D) 3 + sin y = 2 + 6x E) 3 - sin y = 2 + 6x - 1 Answer: C Diff: 1 Var: 1 Section: 8.2

207

+ 6, y(0) = 0. Express the answer as an

10) Find the solution of the IVP A) y = 9 B) y = 2

=

, y(0) = 3. Express the answer as a function of x.

+ 9x + 27 + 3x + 3

C) y = D) y = E) y = Answer: E Diff: 1 Var: 1 Section: 8.2 11) The population of a rabbit colony on an island was 300 in January of 2020 and growing at a rate of 14.9% per year. Assuming an exponential growth model, find the population or rabbits on the island eighteen months later.

A) 375 B) 387 C) 399 D) 411 E) 417 Answer: A Diff: 1 Var: 1 Section: 8.2 12) The population of a rabbit colony on an island was 360 in January of 2020 and growing at a rate of 14.9% per year. Assuming an exponential growth model, how long would it take the population of rabbits to double?

A) 3.91 yr B) 4.15 yr C) 4.38 yr D) 4.65 yr E) 4.89 yr Answer: B Diff: 1 Var: 1 Section: 8.2

208

13) The half-life of radioactive carbon-14 is about 5730 years. If a sample of 84 g of radioactive carbon is locked in a cave until only 67 g remain, for how long has the sample been locked away?

A) 1725 B) 1907 C) 1984 D) 1869 E) 2046 Answer: D Diff: 1 Var: 1 Section: 8.2 14) The half-life of radioactive carbon-14 is about 5730 years. If a sample of 156 g of radioactive carbon is locked in a cave, how much carbon-14 will remain after 9850 years?

A) 47.4 B) 50.5 C) 59.9 D) 65.7 E) 71.3 Answer: A Diff: 1 Var: 1 Section: 8.2

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 209

Chapter 8 8.3

Mathematical Modeling with Differential Equations

Slope Fields; Euler's Method

1) Suppose = 4x + 2y. Find the value of the slope field at (3, -1).

A) 2 B) 10 C) 12 D) 32 E) -382 Answer: B Diff: 1 Var: 1 Section: 8.3 2) Suppose = 3x + 7y. Find the value of the slope field at (-3, -1).

A) -24 B) -27 C) -2 D) -56 E) -136 Answer: C Diff: 1 Var: 1 Section: 8.3 3) Suppose = -6 A) 13 B) 85 C) 98 D) 1 E) -97 Answer: D Diff: 1 Var: 1 Section: 8.3

+ 7 , find the value of the slope field at (1, -1).

4) Suppose = -3 A) 3 B) 18 C) 21 D) 6 E) -15 Answer: E Diff: 1 Var: 1 Section: 8.3

+ 3 , find the value of the slope field at (-1, -2).

5) Suppose

=

, find the value of the slope field at (3, 3).

210

A) -12 B) -72 C) 99 D) E) Answer: E Diff: 2 Var: 1 Section: 8.3 6) Use Euler's method with the step size of △ x = 0.2 to approximate solution to the initial-value problem = -4x + 6y; y(0) = 3 at A) 6.6 B) 18 C) -18 D) 10.8 E) 3.4 Answer: A Diff: 1 Var: 1 Section: 8.3 7) Use Euler's method with the step size of △ x = 0.02 to approximate solution to the initial-value problem = 5x + 2y; y(0) = 5 at A) 10.11 B) 5.2 C) 10.13 D) 14.36 E) 6.93 Answer: B Diff: 2 Var: 1 Section: 8.3

211

8) Use Euler's method with the step size of △ x = 0.01 to approximate solution to the initial-value problem = 0.3x + 0.55y; y(1) = -3 at A) -1.35 B) 1.95 C) -3.0135 D) -0.9035 E) -7.1235 Answer: C Diff: 3 Var: 1 Section: 8.3 9) Use Euler's method with the step size of △ x = 0.1 to approximate solution to the initial-value problem = -2x + 3y; y(0) = 4 at You will need to take two steps here!

A) -12 B) 12 C) 6.74 D) 11.85 E) 2.54 Answer: C Diff: 1 Var: 1 Section: 8.3 10) Use Euler's method with the step size of △ x = 0.02 to approximate solution to the initial-value problem = 4x + 6y; y(1) = 4 at A) 5.1888 B) 28 C) -20 D) 8.2888 E) 3.0788 Answer: A Diff: 2 Var: 1 Section: 8.3

212

11) Use Euler's method with the step size of △ x = 0.05 to approximate solution to the initial-value problem = -0.3x + 0.3y; y(1) = 2 at A) 0.3 B) 2.029475 C) -0.9 D) 6.139475 E) -0.370525 Answer: B Diff: 3 Var: 1 Section: 8.3

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

213

Calculus Early Transcendentals, 12e (Anton) Chapter 8 Mathematical Modeling with Differential Equations 8.4

First-Order Differential Equations and Applications

1) What is the solution to the following differential equation? =6 A) t =

-6

B) t =

+ 36

C) y = D) y = E) y = Answer: D Diff: 2 Var: 1 Section: 8.4 2) What is the solution to the following differential equation? + 7y = A) y =

+C

B) y =

+C

C) y = D) y =

+C

E) y =

+ 10

Answer: D Diff: 2 Var: 1 Section: 8.4

214

3) What is the solution to the following differential equation? + 7y = 21 sin(9x) + 27 cos(9x) A) y = 3 cos(9x) + C B) y = 3 sin(9x) + C C) y = 3 sin(9x) + C D) y = 7 sin(9x) + C E) y = 7 cos(9x) + C Answer: C Diff: 3 Var: 1 Section: 8.4 4) Solve the differential equation. sin x

- 7y cos x = 0

A) y = C B) y = C C) y = C D) y = C E) y = C cos x Answer: A Diff: 1 Var: 1 Section: 8.4

215

5) Solve the IVP x

+ y = x, y(5) = 2

A) y = 2x + B) y =

x-

C) y = 2x D) y =

x+

E) y =

x+

Answer: A Diff: 1 Var: 1 Section: 8.4 6) Solve the IVP A) y = 2

+1

B) y = 2

-1

C) y = 2

-1

D) y = 2

+ 1x

- 2xy = 2x, y(0) = 1

E) y = 2 - 1x Answer: A Diff: 1 Var: 1 Section: 8.4 7) At t = 0, a tank contains 25 oz of salt dissolved in 50 gallons of water. Then brine containing 6 oz salt/gal is allowed to enter the tank at a rate of 2 gal/min and the mixed solution is drained from the tank at the same rate. How much salt is in the tank after 25 minutes?

A) 175 B) 189 C) 199 D) 211 E) 229 Answer: A Diff: 1 Var: 1 Section: 8.4

216

8) At t = 0, a tank is filled with 200 gallons of water with 40 oz of salt dissolved in it. At salt solution containing 5 oz/gal enters the tank at a rate of 2 gal/min. Well-mixed solution leaves the tank at the same rate. How much salt would remain in the tank after 30 min?

A) 323 B) 335 C) 348 D) 365 E) 373 Answer: A Diff: 1 Var: 1 Section: 8.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

217

Calculus Early Transcendentals, 12e (Anton) Chapter 9 Infinite Series 9.1

Sequences

1) Write out the first five terms of the sequence

A) -

,

,-

,

,-

B)

,

,

,

,

C)

,

,

,

,

D) -

,

E)

,-

,

,

, ,

.

,,

Answer: D Diff: 1 Var: 1 Section: 9.1

2) Write out the first five terms of the sequence

A)

,

,

,

,

B)

,

,

,

,

C)

,

,

,

,

D)

,

,

,

,

E)

,

,

,

,

Answer: B Diff: 1 Var: 1 Section: 9.1

218

.

3) Write out the first five terms of the sequence

A)

,

,

,

,

B)

,

,

,

,

C)

,

,

,

,

D)

,

,

,

,

E)

,

,

,

,

Answer: C Diff: 1 Var: 1 Section: 9.1

219

.

4) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence. ,

,

,

A)

B)

C)

D)

E) Answer: D Diff: 1 Var: 1 Section: 9.1

220

,

5) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence. ,

,

,

A)

B)

C)

D)

E) Answer: D Diff: 1 Var: 1 Section: 9.1

221

,

6) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence. ,-

,

,-

A)

B)

C)

D)

E) Answer: C Diff: 2 Var: 1 Section: 9.1

222

,

7) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence.

-

,

,-

A)

B)

C)

D)

E) Answer: D Diff: 2 Var: 1 Section: 9.1

223

,

,-

8) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence. ,

,

,

A)

B)

C)

D)

E) Answer: C Diff: 2 Var: 1 Section: 9.1

224

,

9) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence. ,

,

,

A)

B)

C)

D)

E) Answer: B Diff: 2 Var: 1 Section: 9.1

225

,

10) The following are the first five terms of an infinite sequence. Find a formula for the general term starting with and write down the entire sequence.

-

,

,-

,

,-

A)

B)

C)

D)

E)

or

Answer: E Diff: 3 Var: 1 Section: 9.1

11) What is the limit of the sequence

?

A) B) C) 0 D) E) Does not converge Answer: C Diff: 1 Var: 1 Section: 9.1 226

12) What is the limit of the sequence

?

A) 2 B) C) 0 D) E) Does not converge Answer: A Diff: 2 Var: 1 Section: 9.1

13) What is the limit of the sequence

?

A) B) 3e C) e D) 1 E) Does not converge Answer: A Diff: 3 Var: 1 Section: 9.1

14) What is the limit of the sequence

?

A) B) C) sin 7 D) 0 E) Does not converge Answer: D Diff: 2 Var: 1 Section: 9.1

227

15) What is the limit of the sequence

?

A) B) C) D) 0 E) Does not converge Answer: C Diff: 2 Var: 1 Section: 9.1

16) What is the limit of the sequence

?

A) B) 1 C) 0 D) E) Does not converge Answer: C Diff: 1 Var: 1 Section: 9.1

17) What is the limit of the sequence

?

A) 5 B) C) 1 D) 0 E) Does not converge Answer: D Diff: 1 Var: 1 Section: 9.1 228

18) What is the limit of the sequence

?

A) B) C) 0 D) E) Does not converge Answer: C Diff: 2 Var: 1 Section: 9.1

19) What is the limit of the sequence

?

A) B) C) 0 D) E) Does not converge Answer: E Diff: 2 Var: 1 Section: 9.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

229

Calculus Early Transcendentals, 12e (Anton) Chapter 9 Infinite Series 9.2

Monotone Sequences

1) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.2 2) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2 3) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.2 230

4) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2 5) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2 6) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 1 Var: 1 Section: 9.2

231

7) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.2 8) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 3 Var: 1 Section: 9.2 9) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 3 Var: 1 Section: 9.2

232

10) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.2 11) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.2 12) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2

233

13) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.2 14) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.2 15) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2

234

16) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2 17) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.2 18) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: C Diff: 2 Var: 1 Section: 9.2

235

19) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 3 Var: 1 Section: 9.2 20) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.2 21) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: A Diff: 1 Var: 1 Section: 9.2

236

22) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.2 23) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: B Diff: 3 Var: 1 Section: 9.2 24) Determine which answer best describes the sequence.

A) Strictly increasing B) Strictly decreasing C) Eventually strictly increasing D) Eventually strictly decreasing E) Cannot be determined Answer: C Diff: 3 Var: 1 Section: 9.2 © (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

237

Calculus Early Transcendentals, 12e (Anton) Chapter 9 Infinite Series 9.3

Infinite Series

1) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 11 E) Diverges Answer: B Diff: 1 Var: 1 Section: 9.3 2) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 13 E) Diverges Answer: B Diff: 2 Var: 1 Section: 9.3

238

3) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 2 E) Diverges Answer: E Diff: 2 Var: 1 Section: 9.3 4) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 4 E) Diverges Answer: B Diff: 3 Var: 1 Section: 9.3

239

5) Determine whether or not the following series converges. If it converges, find its sum.

A) B) 9 C) 0 D) E) Diverges Answer: A Diff: 2 Var: 1 Section: 9.3 6) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 3 E) Diverges Answer: E Diff: 2 Var: 1 Section: 9.3

240

7) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: D Diff: 2 Var: 1 Section: 9.3 8) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 13 E) Diverges Answer: E Diff: 2 Var: 1 Section: 9.3

241

9) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: B Diff: 2 Var: 1 Section: 9.3 10) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: C Diff: 2 Var: 1 Section: 9.3

242

11) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: D Diff: 2 Var: 1 Section: 9.3 12) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: A Diff: 2 Var: 1 Section: 9.3

243

13) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) 13 E) Diverges Answer: E Diff: 2 Var: 1 Section: 9.3 14) Determine whether or not the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: B Diff: 3 Var: 1 Section: 9.3

244

15) Which of the following fractions is equivalent to the following repeating decimal?

0.4141 A) B) C) D) E) Answer: A Diff: 1 Var: 1 Section: 9.3 16) Which of the following fractions is equivalent to the following repeating decimal?

0.383383 A) B) C) D) E) Answer: E Diff: 1 Var: 1 Section: 9.3

245

17) Which of the following fractions is equivalent to the given repeating decimal?

9.4343 A) B) C) D) E) Answer: A Diff: 1 Var: 1 Section: 9.3 18) Which of the following fractions is equivalent to the given repeating decimal?

0.758758 A) B) C) D) E) Answer: B Diff: 1 Var: 1 Section: 9.3

246

19) Which of the following fractions is equivalent to the given repeating decimal?

37.2424 A) B) C) D) E) Answer: A Diff: 2 Var: 1 Section: 9.3 20) Express the following repeating decimal as a fraction: 2.593593 A) B) C) D) E) Answer: E Diff: 3 Var: 1 Section: 9.3

247

21) Find the sum of the following geometric series:

A) B) C) D) E) Diverges Answer: E Diff: 2 Var: 1 Section: 9.3 22) Find the sum of the following geometric series:

A) B) 6 C) 3 D) 18 E) Diverges Answer: D Diff: 2 Var: 1 Section: 9.3

248

23) Find the sum of the following geometric series:

A) B) C) D) E) Diverges Answer: B Diff: 2 Var: 1 Section: 9.3 24) Find the sum of the following telescoping series:

A) B) C) D) E) Diverges Answer: C Diff: 3 Var: 1 Section: 9.3

249

25) Determine whether the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: D Diff: 1 Var: 1 Section: 9.3 26) Determine whether the following series converges. If it converges, find its sum.

A) B) C) D) E) Diverges Answer: B Diff: 2 Var: 1 Section: 9.3

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

250

Calculus Early Transcendentals, 12e (Anton) Chapter 9 Infinite Series 9.4

Convergence Tests

1) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 1 Var: 1 Section: 9.4 2) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.4 3) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.4

251

4) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.4 5) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.4 6) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 2 Var: 1 Section: 9.4 7) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 3 Var: 1 Section: 9.4

252

8) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 3 Var: 1 Section: 9.4 9) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 3 Var: 1 Section: 9.4 10) Determine whether or not the following series converges. (Hint: Use the integral test.)

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 1 Var: 1 Section: 9.4 11) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.4

253

12) Determine whether or not the following series converges.

A) Diverges B) Converges C) Cannot be determined Answer: A Diff: 2 Var: 1 Section: 9.4 13) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: A Diff: 3 Var: 1 Section: 9.4 14) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 1 Var: 1 Section: 9.4

254

15) Determine whether or not the following series converges.

A) Converges B) Diverges C) Cannot be determined Answer: B Diff: 3 Var: 1 Section: 9.4

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 255

Chapter 10 10.1

Parametric and Polar Curves; Conic Sections

Parametric Equations; Tangent Lines and Arc Length for Parametric Curves

1) For the parametric curve: x = 2t + 1, y = 8t + 1, eliminate the parameter and express in rectangular form.

A) y = 4x + 3 B) y = 4x - 5 C) y = 4x - 3 D) y = 2x - 5 E) y = 16x - 3 Answer: C Diff: 1 Var: 1 Section: 10.1 2) For the parametric curve: x = 5 cos t, y = 5 sin t, eliminate the parameter and express in rectangular form.

A) + =5 B) 6 + 6 = 25 C) + =1 D) = 25 E) + = 25 Answer: E Diff: 2 Var: 1 Section: 10.1 3) For the parametric curve: x = rectangular form.

A) y = 5x - 10 B) y = 5 - 10 C) y = 5 - 10 D) y = 5 - 10

,y=5

- 10, eliminate the parameter and express in

E) y = 25 - 10 Answer: B Diff: 2 Var: 1 Section: 10.1

256

4) For the parametric curve: x = 2 + 4 cos t, y = 5 + 5 sin t, eliminate the parameter and express in rectangular form.

A)

-

=1

B)

-

=1

C)

+

=1

D)

+

=1

E)

-

=1

Answer: C Diff: 3 Var: 1 Section: 10.1 5) For the parametric curve: x = 16 , y = 8t, eliminate the parameter and express in rectangular form.

A) y = 8 B) y = 2 C) y = 2 D) y = E) y = 16 Answer: B Diff: 2 Var: 1 Section: 10.1

257

6) For the parametric curve: x =

,y=

eliminate the parameter and express in

rectangular form.

A) + =1 B) y =

C) y =

D) y =

E) y = Answer: A Diff: 3 Var: 1 Section: 10.1 7) Put the rectangular equation y =2 A) x = 2t, y = +7 B) x = t + 7, y = 2 C) x = , y = 2 + 7 D) x = t, y = 2 + 7 E) x = 2 , y = +7 Answer: D Diff: 2 Var: 1 Section: 10.1

+ 7 into parametric form.

8) For the parametric curve: x = 3t - 4, y = 6t + 5, eliminate the parameter and express in rectangular form.

A) y = 2x - 3 B) y = 2x + 13 C) y = 2x - 11 D) y = 15x + 13 E) y = 3x + 15 Answer: B Diff: 1 Var: 1 Section: 10.1

258

9) For the parametric curve: x = 4 cos 5t, y = 4 sin 5t, eliminate the parameter and express in rectangular form.

A) + =4 B) =4 C) + = 16 D) 4 + 4 = 5 E) + = 25 Answer: B Diff: 2 Var: 1 Section: 10.1 10) For the parametric curve: x = rectangular form.

A) y = 1.25 + 2 B) y = 1.25 + 2 C) y = 1.67 + 2x D) y = 1.67 + 2x E) y = 1.25 + 2 Answer: A Diff: 2 Var: 1 Section: 10.1

,y=5

+ 2, eliminate the parameter and express in

11) For the parametric curve: x = 4 + 3 cos(πt), y = 5 + 2 sin(πt), eliminate the parameter and express in rectangular form.

A)

+

=1

B)

+

=1

C)

+

=1

D)

-

=1

E)

+

=1

Answer: C Diff: 3 Var: 1 Section: 10.1

259

12) For the parametric curve: x = 5t, y = 2 , eliminate the parameter and express in rectangular form.

A) y =

- 10x

B) y =

- 10

C) y =

+ 10x

D) y =

+ 10

E) y =

+ 10

Answer: B Diff: 2 Var: 1 Section: 10.1 13) For the parametric curve: x = 3 , y = 27 rectangular form.

A) y = 3 + 3x

+ 9 , eliminate the parameter and express in

B) y = 9 + 9x C) y = 9 + 3x D) y = 9 + 3 E) y = 3 + 3 Answer: A Diff: 2 Var: 1 Section: 10.1 14) Create the parametric equation to describe a circle of radius 4 oriented clockwise.

A) x = sin t + 4, y = cos t + 4 B) x = sin (4t), y = cos (4t) C) x = cos (4t), y = sin (4t) D) x = 4 sin t, y = 4 cos t E) x = cos

, y = sin

Answer: E Diff: 2 Var: 1 Section: 10.1

260

15) For the parametric equation x = 2t + 10, y = 6t - 4, the value of

at t = -4 is

A) 2 B) 10 C) 3 D) 4 E) 0 Answer: A Diff: 2 Var: 1 Section: 10.1 16) For the parametric equation x = 3

+ 12, y = 2

A) 4 B) 3 C) -4 D) 12 E) 2 Answer: A Diff: 2 Var: 1 Section: 10.1 17) Find

if x = cos t, y = 11 sin t

A) 11 tan t B) 11 cot t C) -11 tan t D) -11 cot t E) 11 sec t Answer: D Diff: 1 Var: 1 Section: 10.1 18) Find

, if x = sin t, y = 12 cos t

A) -12 t B) 12 cot t C) -12 cot t D) 12 sec t E) 12 csc t Answer: A Diff: 2 Var: 1 Section: 10.1

261

- 2, the value of

at t = 4 is

19) Find the value(s) of t for which the tangents to x = sin t, y= 7 A)

+ 20 is/are horizontal.

,

B) 0 C) D) 0,

,

E) π Answer: B Diff: 3 Var: 1 Section: 10.1 20) Find

at the point where θ =

if x = 10 + 3 cos θ, y= sin θ.

A) -10 B) 10 C) 1 D) E) 0 Answer: D Diff: 2 Var: 1 Section: 10.1 21) Find the equation of the tangent to the curve x = 2 A) y =

x - 540

B) y =

x - 580

C) y =

x - 564

D) y =

x + 540

E) y =

x - 440

Answer: A Diff: 3 Var: 1 Section: 10.1

262

+ 7t, y = 5

+ 6t at t = 2.

22) Find

at the point where t =

if x = -8 + 4 cos t, y = 3 sin t

A) B) C) D) E) Answer: C Diff: 2 Var: 1 Section: 10.1 23) Find the exact arc length of x = 8 sin (3t), y = 8 cos (3t) , over the interval 0 ≤ t ≤

.

A) 48π B) 24π C) 12π D)

π

E)

π

Answer: C Diff: 3 Var: 1 Section: 10.1

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Calculus Early Transcendentals, 12e (Anton) 263

Chapter 10 10.2

Parametric and Polar Curves; Conic Sections

Polar Coordinates

1) Find the rectangular coordinates of the point whose polar coordinates are given.

(4, 14π) A) (1, 4) B) (1, 14) C) (14, 0) D) (4, 0) E) (0, 4) Answer: D Diff: 1 Var: 1 Section: 10.2 2) Find the rectangular coordinates of the point whose polar coordinates are given.

A) (1, 1) B) (0, 11) C) (-1, 0) D) (11, 0) E) (0, -1) Answer: E Diff: 2 Var: 1 Section: 10.2 3) State the name that describes the polar curve most precisely. r = 7 - 7 sin θ A) cardioid B) rose C) spiral D) lemniscate E) line Answer: A Diff: 2 Var: 1 Section: 10.2

264

4) State the name that describes the polar curve most precisely. r= A) cardioid B) lemniscate C) rose D) spiral E) line Answer: D Diff: 2 Var: 1 Section: 10.2 5) State the name that describes the polar curve most precisely. r = sin(5θ) A) cardioid B) line C) spiral D) lemniscate E) rose Answer: E Diff: 2 Var: 1 Section: 10.2 6) State the name that describes the polar curve most precisely. r= A) cardioid B) lemniscate C) line D) circle E) spiral Answer: D Diff: 3 Var: 1 Section: 10.2 7) State the name that describes the polar curve most precisely. r = -5 sec θ A) line B) cardioid C) lemniscate D) circle E) spiral Answer: A Diff: 2 Var: 1 Section: 10.2 265

8) Which equation below most closely represents the graph shown.

A) r = 6 sin θ B) r = 6θ C) r = 6 cos θ D) r = 6(1 - sin θ) E) r = 6(1 - cos θ) Answer: B Diff: 2 Var: 1 Section: 10.2 9) Which equation below most closely represents the graph shown.

A) r = 9 sin 2θ B) r = 9θ C) r = 9 cos 2θ D) r = 9(1 - sin θ) E) r = 9(1 - cos θ) Answer: C Diff: 2 Var: 1 Section: 10.2

266

10) What are the polar coordinates of a point whose rectangular coordinates are given as Note: n is an integer.

A) B) C) D) (6, 6) E) (0, 1) Answer: B Diff: 3 Var: 1 Section: 10.2 11) What are the polar coordinates of a point whose rectangular coordinates are given as Note: n is an integer.

A) B) C) D) (10, 10) E) (0, 1) Answer: C Diff: 3 Var: 1 Section: 10.2

267

12) What are the polar coordinates of a point whose rectangular coordinates are given as (4, -4)?

Note: n is an integer.

A) B) C) D) E) (0, 1) Answer: D Diff: 3 Var: 1 Section: 10.2

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268

Calculus Early Transcendentals, 12e (Anton) Chapter 11 Three-dimensional Space; Vectors 11.1

Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

1) The distance from (6, 8, 11) to the xy-plane is A) 6 B) 8 C) 11 D) 14.866069 E) 10 Answer: C Diff: 1 Var: 1 Section: 11.1 2) The distance from (6, 0, 8) to the origin is A) 100 B) 36 C) 110 D) 10 E) 210 Answer: D Diff: 1 Var: 1 Section: 11.1 3) The distance from (-5, -4, -3) to the origin is approximately A) 2500.00 B) 1681.00 C) 2507.07 D) 7.07 E) 5007.07 Answer: D Diff: 1 Var: 1 Section: 11.1 4) The surface described by A) a point B) a parabola C) a circle D) a sphere E) a line Answer: D Diff: 1 Var: 1 Section: 11.1

+

+

269

is

5) The spherical surface A) (0, 0, 0) B) (1, 1, 1) C) (4, -5, 5) D) (-4, 5, -5) E) (4, 4, 4) Answer: D Diff: 1 Var: 1 Section: 11.1 6) The graph of + A) line x = z B) line x = y C) x-axis D) y-axis E) z-axis Answer: E Diff: 2 Var: 1 Section: 11.1

+

+

is centered at

= 3 is an infinitely long cylinder whose central axis is the

7) The equation for the cylinder with radius 4 oriented symmetric about the z-axis is A)

+

=4

B)

+

= 16

C)

=4

D)

= 16

E) 4 + 4 = 1 Answer: B Diff: 2 Var: 1 Section: 11.1 8) The equation for the cylinder with radius 4 oriented symmetric about the x-axis is A)

+

B)

+

C)

=4

D)

= 16

= 16 = 16

E) 4 + 4 = 1 Answer: A Diff: 2 Var: 1 Section: 11.1

270

9) The equation for the cylinder with radius 7 oriented symmetric about the y-axis is A)

+

B)

+

C)

=4

D)

= 16

= 49 = 49

E) 7 + 7 = 1 Answer: B Diff: 2 Var: 1 Section: 11.1 10) The distance from the sphere A) 6 B) 5 C) 0 D) 11 E) 1 Answer: B Diff: 3 Var: 1 Section: 11.1

+

11) The sphere represented by A) (5, -5, 0) B) (0, 0, 0) C) (-5, 5, 0) D) (4, 6, 0) E) (-4, -6, 0) Answer: A Diff: 3 Var: 1 Section: 11.1

- 10x +

+

= 1 to the point (0, 0, 6) is

+ 10y +

= 3 has center

12) Find the equation of the sphere with a diameter whose endpoints are (8, 10, 10) and (0, 0, 0).

A)

-

+

= 66

B)

+

+

= 66

C)

+

+

= 66

D)

+

E) Answer: C Diff: 2 Var: 1 Section: 11.1

+

= 66

+

= 66

271

13) Find the equation of the sphere with a diameter whose endpoints are (2, 1, 4) and (10, 9, 8).

A)

-

+

= 36

B)

+

+

= 36

C)

+

+

= 36

D)

+

+

= 36

+

= 36

E) Answer: B Diff: 2 Var: 1 Section: 11.1

14) The distance from (7, 9, 12) to the xz-plane is A) 7 B) 9 C) 12 D) 16.552945 E) 11.401754 Answer: B Diff: 1 Var: 1 Section: 11.1 15) The distance from (5, 7, 10) to the yz-plane is A) 5 B) 7 C) 10 D) 13.190906 E) 8.602325 Answer: A Diff: 1 Var: 1 Section: 11.1

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

272

Calculus Early Transcendentals, 12e (Anton) Chapter 11 Three-dimensional Space; Vectors 11.2

Vectors

1) What are the components of v. v = <-7, -1>?

A) -7 and -1 B) -1 and -8 C) -8 and -6 D) 0 and 0 E) and 0 Answer: A Diff: 1 Var: 1 Section: 11.2 2) What are the components of v. v = <2, -8, -6>?

A) 0 and 0 B) -8 and -6 C) -6 and 10 D) 2, -8, and -6 E) and 0 Answer: D Diff: 1 Var: 1 Section: 11.2 3) Find the components of the vector

if

= (5, 3), and

if

= (-3, -6, 7), and

= (10, 4).

A) <5, 4> B) <5, 1> C) <0, 0> D) <50, 10> E) <10, 3> Answer: B Diff: 1 Var: 1 Section: 11.2 4) Find the components of the vector A) <-3, 5, -9> B) <-2, 11, -16> C) <0, 0, 0> D) <-25, -6, 21> E) <-3, -6, 7> Answer: B Diff: 2 Var: 1 Section: 11.2

273

= (-5, 5, -9).

5) Find the norm of v. v = <2, 9> A) 42.5 B) 85 C) D) 0 E) Answer: E Diff: 1 Var: 1 Section: 11.2 6) Find the norm of v. v = <2, 3, 3> A) B) 10 C) D) E) 5 Answer: D Diff: 1 Var: 1 Section: 11.2 7) If u = 5i + 3j + 5k, and v = 3i - 4j + 2k, v - u = A) 3i B) 5i C) -2i - 7j - 3k D) 3i - 6j - 2k E) 5i + 6j + 2k Answer: C Diff: 2 Var: 1 Section: 11.2 8) If u = 6i - 3j + k, and v = i + 3j - k, u - v = A) 5i B) 6i C) 5i + 6j + 2k D) 5i - 6j + 2k E) 6i + 6j + 2k Answer: D Diff: 2 Var: 1 Section: 11.2

274

9) If u = 2i + 4j + 2k, 5u = A) 8i + 2j + 6k B) 10i + 20j + 10k C) 10i + 2j + 6k D) 10i + 2j + 20k E) 8i + 10j + 6k Answer: B Diff: 2 Var: 1 Section: 11.2 10) If u = -8i + 5j + 4k, 7u = A) 13i + 13j - 3k B) -56i + 35j + 28k C) -56i + 13j - 3k D) -56i + 13j + 35k E) 13i - 56j - 3k Answer: B Diff: 2 Var: 1 Section: 11.2 11) Let u = 7i - 6j. Find the vector in the same direction as u with twice the length of u.

A) 14i B) 7i C) 14i + 9j + 3k D) 14i - 12j E) 14i + 12j Answer: D Diff: 2 Var: 1 Section: 11.2 12) Suppose u = 5i + 13j. Find the vector in the same direction as u with twice the length of u.

A) 13i B) 5i C) 10i + 26j D) 13i - 12j E) 13i + 12j Answer: C Diff: 2 Var: 1 Section: 11.2

275

13) Let u = <-2, -7>, and v = <-5, -6>. Find the vector x that satisfies x = 5u + 4v.

A) <-11, -9> B) <-30, -59> C) <-9, -11> D) <-10, -18> E) <-59, -30> Answer: B Diff: 2 Var: 1 Section: 11.2 14) Find a unit vector in the direction of a = <-8, -1, -7>.

A) B) C) D) E) Answer: D Diff: 1 Var: 1 Section: 11.2 15) Let u = <4, 3>, and v = <4, -1>. Find the vector x that satisfies x = 3u - 7v.

A) <3, 7> B) <-16, 16> C) <7, 3> D) <8, -3> E) <16, -16> Answer: B Diff: 2 Var: 1 Section: 11.2

276

16) In the figure below, the 500 lb traffic light is supported by two flexible cables. The tension in each cable act as forces oriented in the cable directions and directed from the traffic light and towards the wall. What are the magnitude of force in lb of the 30 and 45 oriented cables, respectively

A) 30° cable 336, 45° cable 448 B) 30° cable 250, 45° cable 250 C) 30° cable 286, 45° cable 498 D) 30° cable 448, 45° cable 336 E) 45° cable 448, 45° cable 336 Answer: B Diff: 2 Var: 1 Section: 11.2

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Calculus Early Transcendentals, 12e (Anton) 277

Chapter 12 12.1

Vector-Valued Functions

Introduction to Vector-Valued Functions

1) Find the domain of r(t) = 2 A) (-∞, ∞), r(0) = 2i B) (-∞, ∞), r(0) = i C) (0, ∞), r(0) = 2i D) (-∞, ∞), r(0) = 2j E) [0, ∞), r(0) = 2i Answer: A Diff: 1 Var: 1 Section: 12.1

i - 2t

j and calculate r(0).

2) Find the domain of r(t) = (1 + sin t)i - 6t j and calculate r(π).

A) 0 ≤ t < ∞, r(π) = 2i - 6πj B) -∞ < t < ∞, r(π) = i - 6πj C) 0 ≤ t ≤ 2π, r(π) = 6πj D) -π ≤ t ≤ π, r(π) = i - j E) 0 < t < ∞, r(π) = i - 6j Answer: B Diff: 1 Var: 1 Section: 12.1 3) Find the domain of r(t) = A) 0 ≤ t < ∞, r(3) = 2i - 2πj B) -∞ < t < ∞, r(3) = i - 2πj C) t ≤ D) -

∪ ≤t≤

≤ t, r(3) = , r(3) =

i - 2t j and calculate r(3).

i + 6j i - 6j

E) 0 < t < ∞, r(3) = i - 2j Answer: D Diff: 2 Var: 1 Section: 12.1

278

4) Describe the graph of r(t) = 5i + 10j + 12k.

A) Twisted cubic B) Single point C) Spiral D) Parabola E) Circle Answer: B Diff: 2 Var: 1 Section: 12.1 5) Describe the graph of r(t) = 5i + cos t j + sin t k.

A) Twisted cubic B) Straight line C) Spiral D) Parabola E) Circle Answer: E Diff: 2 Var: 1 Section: 12.1 6) Describe the graph of r(t) = 6i + 11 sin t j + 13 cos t k.

A) Twisted cubic B) Straight line C) Spiral D) Parabola E) Ellipse Answer: E Diff: 2 Var: 1 Section: 12.1 7) Describe the graph of r(t) = 11t i + 16 sin t j - 18 cos t k.

A) Twisted cubic B) Straight line C) Spiral D) Parabola E) Circle Answer: C Diff: 2 Var: 1 Section: 12.1

279

8) Describe the graph of r(t) = 11 A) Twisted cubic B) Straight line C) Spiral D) Parabola E) Circle Answer: A Diff: 2 Var: 1 Section: 12.1 9) Describe the graph of r(t) = A) Twisted cubic B) Straight line C) Spiral D) Parabola E) Circle Answer: D Diff: 3 Var: 1 Section: 12.1

i + 16

j - 18t k.

i + 6 t j - 3k.

10) At t increases, the graph of r(t) = 2 cos t i + 7 sin t j - 9t k sketches A) Clockwise and up B) Counter-clockwise and up C) Clockwise and down D) Counter-clockwise and down E) In a circle Answer: D Diff: 2 Var: 1 Section: 12.1 11) At t increases, the graph of r(t) = 10 cos t i + 15 sin t j + 17t k sketches A) Clockwise and up B) Counter-clockwise and up C) Clockwise and down D) Counter-clockwise and down E) In a circle Answer: B Diff: 2 Var: 1 Section: 12.1

280

12) At t increases, the graph of r(t) = 4 sin t i + 9 cos t j - 11t k sketches A) Clockwise and up B) Counter-clockwise and up C) Clockwise and down D) Counter-clockwise and down E) In a circle Answer: C Diff: 2 Var: 1 Section: 12.1 13) Find the parametric equations that correspond to the given vector equation: A) x = sin t, y = cos t, z = -t B) x = 4 sin t , y = 9 cos t , z = 11t C) x = 4 sin t , y = 9 cos t , z = -11t D) x = 4 cos t , y = 9 sin t , z = -11t E) x = sin t, y = cos t, z = t Answer: C Diff: 1 Var: 1 Section: 12.1 14) Find the parametric equations that correspond to the given vector equation: A) x = sin t, y = cos t, z = -t B) x = 6 t , y = 11 t , z = -13 C) x = 6 sin t , y = 11 cos t , z = -13t D) x = 6 cos t , y = 11 sin t , z = -13t E) x = 6 t , y = 11 t , z = 13 Answer: B Diff: 1 Var: 1 Section: 12.1

281

15) Write down parametric equations representing the intersection curve of the following surfaces.

Use parameter 81

+

+ 81

= 162, and y = 162

for z > 0.

A) x = t, y = 162, z = B) x = t, y = 162 , z = 2 - 324 C) x = t, y = 162 , = 2 - t - 324 D) x = t, y = 162 , z = 2 + + 324 E) x = t, y = 162 , z = Answer: E Diff: 3 Var: 1 Section: 12.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

282

Calculus Early Transcendentals, 12e (Anton) Chapter 12 Vector-Valued Functions 12.2

Calculus of Vector-Valued Functions

1)

2 i + 3 ln t j =

A) 18i - 9j B) 18i + 9j C) not defined D) 27 E) 0 Answer: B Diff: 1 Var: 1 Section: 12.2 2)

8 i + 7 ln t j =

A) 72i - 21j B) 72i + 21j C) not defined D) 93 E) 0 Answer: C Diff: 3 Var: 1 Section: 12.2 3) If r(t) = (11 + 8t) i + A) 11 i + B)

j, find

(t).

j i+

j

C) 8t i + 14t j D) 56 + 77 - 24t - 33 E) 4t i + 4t j Answer: C Diff: 1 Var: 1 Section: 12.2

283

4) If r(t) = (5 + 2t) i + A) 5 i + B)

j+

k, find

j + 2k i+

j

C) 10 + 25 - 12t - 30 D) 2i + 10t j + 2t k E) 4t i + 4t j + 2t k Answer: D Diff: 1 Var: 1 Section: 12.2 5) If r(t) = 8t i + cos t j + k, find A) 8i - j B) 8i + j C) -8i - j D) 8i - j + k E) 8i + j + k Answer: A Diff: 2 Var: 1 Section: 12.2

(π/2).

6) If r(t) = 4t i - 3t j + sin t k, find A) 4i - 3 j - cos t k B) 4i - 3 j + cos t k C) -12 cos t D) 12 cos t E) 12 sin t Answer: B Diff: 2 Var: 1 Section: 12.2

(t).

7) If r(t) = 11 i - 3t j + 6 cos t k, find A) 11 i - 3 j + 6 sin t k B) 11 i - 3 j - 6 sin t k C) 11i - 3 j - 6 sin t k D) 11 i - 6 sin t k E) 11 i - 3 j - 6 sin t k Answer: B Diff: 2 Var: 1 Section: 12.2

(t).

284

(t).

8) If r(t) = 6 i - 3t ln t j + 9t cos t k, find (t).

A) 6 i - 3t ln t j + 9 sin t k B) 6(t - 1) i - 3(t ln t - 1)j - 9(t sin t + t)k C) 6 i - 3j + 9(cos t + t sin t)k D) 6(t + 1) i - 3(ln t + 1)j + 9(cos t + t sin t)k E) 6(t + 1) i - 3(ln t + 1)j + 9(cos t - t sin t)k Answer: E Diff: 3 Var: 1 Section: 12.2 9) If r(t) = i+ j + sin(2t)k, find A) (t) = (13t - 7) i + (11t + 2) j + 2 cos(2t)k B) (t) = (18t - 7) i - (16t + 2) j + 2 cos(2t)k C) (t) = (18t - 7) i + (16t + 2) j + 2 cos(2t)k D) (t) = (18t - 9) i + (16t + 2) j + 2 sin(2t)k E) (t) = (18t - 7) i + (16t + 2) j + 11 cos(2t)k Answer: B Diff: 2 Var: 1 Section: 12.2 10) Where is r(t) = 11 sin t i + A) -∞ < t < ∞ B) 0 < t < ∞ C) 0 ≤ t < ∞ D) 11 E) 0 Answer: A Diff: 1 Var: 1 Section: 12.2

j continuous?

11) Where is r(t) = 2 sin t i + ln t j continuous?

A) -∞ < t < ∞ B) 0 < t < ∞ C) -∞ ≤ t < ∞ D) 2 E) 0 Answer: B Diff: 1 Var: 1 Section: 12.2

285

(t).

12)

dt =

A) <-4, 4> B) <-4, -4> C) <4, 4> D) <4, -4> E) <0, 0> Answer: C Diff: 2 Var: 1 Section: 12.2 13)

dt =

A) <-10, 15> B) <-10, -15> C) <10, 15> D) <10, -15> E) <0, 0> Answer: A Diff: 2 Var: 1 Section: 12.2 14)

dt =

A) <24

+ 11, 24

- 6, 2

>

B) <22

+ 11, 24

- 6, 2

>

C) <22

- 11, -24

+ 6, 2

>

D) <22 + 11, 22 E) <0, 0, 0> Answer: C Diff: 3 Var: 1 Section: 12.2

- 6, 2

>

286

15)

=

A) 81 - 162 - 128 B) 81 - 162 - 162 C) 81 - 162 - 128 D) 81 - 128 - 162 E) 81 - 162 - 162 Answer: C Diff: 3 Var: 1 Section: 12.2

- 128 - 162 + 64 + 64 + 64

+ 64 - 162 + 49 - 128 + 49

16) If r(t) = 7 i + 7 sin t j + 2 cos t k, find A) 14πi + 7j B) 14πi + 7j - 2πk C) 14πi + 7j + 2πk D) 14πi - 7j E) 14πi - 7j - 2πk Answer: D Diff: 1 Var: 1 Section: 12.2 17) Find

(π).

<8, 8 cos t, 4 sin t>

A) <8, -8, 0> B) <8, 8, 4> C) <8, -8, -4> D) <8, 0, 4> E) <8, 0, -4> Answer: A Diff: 1 Var: 1 Section: 12.2 18) Find

<3, 7t, 8 cos t>

A) <3, -7π, 0> B) <3, 7π, 8> C) <3, 7π, 0> D) <3, 7π, -8> E) <3, 7, -8π> Answer: D Diff: 1 Var: 1 Section: 12.2

287

19) Find

<6, 8 sin t, 8 cos t>

A) <6, 0, 8> B) <6, 8, -8> C) <6, 0, 0> D) <6, 0, -8> E) <6, 1, 8> Answer: A Diff: 1 Var: 1 Section: 12.2 20) Evaluate the integral: A)

i+

dt j

B) 3 i + 3t j C) i+

j

D)

i+

j

E)

i+

j

Answer: B Diff: 2 Var: 1 Section: 12.2 21) Let r(t) = <7 + 6t, 2> sin t. Find the equation of the line tangent to the graph of r(t) at the point Write your answer using parametric equations.

A) x = t, y = 21t B) x = t, y =

t

C) x = t, y = 3t D) x = t, y =

t

E) x = t, y =

t

Answer: B Diff: 1 Var: 1 Section: 12.2

288

22) If A)

(t) = 6t i + 9 i+

B)

i+

C)

i+

j, and y(0) = 3 i + 4 j, find y(t). j j j

D) 3 i + 3 j E) 6i + 12j Answer: B Diff: 3 Var: 1 Section: 12.2

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289

Calculus Early Transcendentals, 12e (Anton) Chapter 12 Vector-Valued Functions 12.3

Change of Parameter; Arc Length

1) Find the arc length of the graph of A) 10 B) -6 C) 21 D) -21 E) 0 Answer: A Diff: 1 Var: 1 Section: 12.3 2) Find the arc length of the graph of A) π B) 2π C) 0 D) 1 E) 4 Answer: A Diff: 2 Var: 1 Section: 12.3 3) Find the arc length of the graph of A) π B) π C) 0 D) π E) 4 Answer: B Diff: 2 Var: 1 Section: 12.3 4) Find the arc length of the graph of r(t) = 3 sin t i + 3 cos t j +2t k; 0 ≤ t ≤ 2π.

A) 2 B) π C) 0 D) π E) 4 Answer: B Diff: 2 Var: 1 Section: 12.3

290

5) Find the arc length of the graph of r(t) = (15 sin t)i + (15 cos t)j + 10 A) 2 B) π C) 10

k;

D) 10 E) 10 Answer: C Diff: 2 Var: 1 Section: 12.3 i + 2 j + 2 k; 0 ≤ t ≤ 1.

6) Find the arc length of the graph of r(t) = A) 3e B) 5e - 5 C) 3e - 5 D) e-1-2 E) 3e + 3 Answer: C Diff: 2 Var: 1 Section: 12.3

7) Find the arc length of the graph of r(t) = 5 i + 2 j + 3 k; 0 ≤ t ≤ 1.

A) 3 B) C) 6.164 D) E) Answer: C Diff: 2 Var: 1 Section: 12.3

291

8) Find the arc length of the graph of r(t) = t i +

j + 6k; 1 ≤ t ≤ 2.

A) 3 B) 6.1798 C) 5.618 D) 5.0562 E) 5.418 Answer: C Diff: 3 Var: 1 Section: 12.3 9) Find the arc length parameterization of the curve given by x = 2 cos t + 8, y = 2 sin t - 10 that has the same orientation and uses (8, -10) as a reference point.

A) x = 2 sin

+ 8, y = 2 cos

- 10

B) x = cos(s) + 8, y = sin(s) - 10 C) x = cos

+ 8, y = sin

- 10

D) x = 2 cos(s) + 8, y = 2 sin(s) - 10 E) x = 2 cos

- 8, y = 2 sin

+ 10

Answer: A Diff: 3 Var: 1 Section: 12.3 10) Find the arc length parameterization of the curve given by x = 2 sin t + 9, y = 2 cos t - 11 that has the same orientation and uses (9, -11) as a reference point.

A) x = 2 sin

+ 9, y = 2 cos

- 11

B) x = sin(s) + 9, y = cos(s) - 11 C) x = sin

+ 9, y = cos

- 11

D) x = 2 sin(s) + 9, y = 2 cos(s) - 11 E) x = 2 sin

- 9, y = 2 cos

+ 11

Answer: A Diff: 3 Var: 1 Section: 12.3

292

11) Find the arc length parameterization of the line x = 4t + 12, y = 6t - 14 that has the same orientation as the given curve and uses (12, -14) as a reference point.

A) x =

+ 12, y =

- 14

B) x =

+ 12, y =

- 14

C) x =

- 12, y =

+ 14

D) x =

+ 12, y =

- 14

E) x =

- 12, y =

+ 14

Answer: D Diff: 3 Var: 1 Section: 12.3 12) Find the arc length parameterization of the line x = 4t - 2, y = 6t + 4 that has the same orientation as the given curve and uses (2, -4) as a reference point.

A) x =

+ 2, y =

-4

B) x =

+ 2, y =

-4

C) x =

- 2, y =

+4

D) x =

+ 2, y =

-4

E) x =

- 2, y =

+4

Answer: C Diff: 3 Var: 1 Section: 12.3

293

13) Find the arc length of the graph of r(t) = 4 cos t i + (4 sin t + 6)j + 4t k on the interval A) 4 B) 8 C) D) 14 E) Answer: C Diff: 3 Var: 1 Section: 12.3 14) Find the arc length of the graph of r(t) = 5 cos t i + (5 sin t + 8)j + 2t k on the interval A) 5π B) 7 C) 7π D) π E) Answer: D Diff: 3 Var: 1 Section: 12.3 15) Find parametric equations for r(t) = 4t i + 7j using arc length, s, as a parameter. Use the point on the curve where as the reference point.

A) x = 4, y = s B) x = 4, y = 7s C) x = s, y = 7s D) x = s, y = 7 E) x = 4s, y = 7 Answer: D Diff: 3 Var: 1 Section: 12.3

294

16) Find the arc length of the parametric curve x = 5 sin t, y = 5 cos t, z = 4, 0 ≤ t ≤ 2π A) 10π B) 5π C) 2π D) E) Answer: A Diff: 3 Var: 1 Section: 12.3

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Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

295

Calculus Early Transcendentals, 12e (Anton) Chapter 13 Partial Derivatives 13.1

Functions of Two or More Variables

1) Let f (x, y, z) = 3 A) -9 B) 13 C) 11 D) 28 E) -15 Answer: C Diff: 1 Var: 1 Section: 13.1 2) Let f (x, y, z) = A) B) C) D) E) Answer: B Diff: 1 Var: 1 Section: 13.1 3) Let f (x, y, z) =

+2

+ 3. Find f (4, -5, -2).

. Find f (-2, 1, 1).

. Find f (1, 3, 5).

A) 0.026974 B) 0.026316 C) 16.2 D) 10.255 E) -23.633684 Answer: B Diff: 1 Var: 1 Section: 13.1

296

4) The level curve of z = 7 A) a circle of radius 4 B) an ellipse C) a circle of radius 16 D) a point E) a hyperbola Answer: B Diff: 1 Var: 1 Section: 13.1

+5

when z = 5 is

5) The level curve of z = 9 A) a parabola B) an ellipse C) a circle D) a point.

E) a hyperbola Answer: A Diff: 1 Var: 1 Section: 13.1

- 7y when z = 1 is

6) The level curve of z = 3 A) a circle of radius 4 B) an ellipse C) a hyperbola D) a point E) a circle Answer: C Diff: 1 Var: 1 Section: 13.1

-4

7) Let f (x, y, z) = 4 + 5 A) 4 + 5 - 3 = 69

- 3 . Find an equation of the level surface passing through

when z = 5 is

B) 4 + 5 - 3 = 162 C) 4 + 5 - 3 = 231 D) 4 + 5 - 3 = 206 E) 4 + 5 - 3 = 18 Answer: B Diff: 2 Var: 1 Section: 13.1

297

8) Let f (x, y, z) = 3 + 4 - 4 . Describe the level surface passing through A) Hyperboloid of two sheets B) Hyperboloid of one sheet C) Elliptical cone D) Elliptic paraboloid E) Hyperbolic paraboloid Answer: B Diff: 2 Var: 1 Section: 13.1 9) Let f (x, y, z) = 4 + 2 + 5 . Describe the level surface passing through A) Ellipsoid B) Hyperboloid of one sheet C) Elliptical cone D) Elliptic paraboloid E) Hyperbolic paraboloid Answer: A Diff: 2 Var: 1 Section: 13.1 10) Let f (x, y, z) = 3 - 2 - 5 . Describe the level surface passing through A) Ellipsoid B) Hyperboloid of one sheet C) Elliptical cone D) Hyperboloid of two sheets E) Hyperbolic paraboloid Answer: D Diff: 2 Var: 1 Section: 13.1 11) Let f (x, y, z) = 5 - 4 - 5 . Describe the level surface passing through A) Ellipsoid B) Hyperboloid of one sheet C) Elliptical cone D) Cone E) Hyperbolic paraboloid Answer: D Diff: 2 Var: 1 Section: 13.1

298

12) Let f (x, y, z) = A) = B) = C) = D) = E) = Answer: D Diff: 2 Var: 1 Section: 13.1

. Describe the level surface passing through

13) What is/are the domain restriction(s) for f (x, y) =

?

A) x > 0, y ≠ 0 B) x > 0 and y > 0, or x < 0 and y < 0 C) x ≠ 0, y ≠ 0 D) No restrictions exist E) x ≠ 0, y < 0 Answer: B Diff: 1 Var: 1 Section: 13.1 14) What is/are the domain restriction(s) for f (x, y) = ln

?

A) x > 0, y ≠ 0 B) x > 0, y > 0 C) x ≠ 0, y ≠ 0 D) No restrictions exist E) x ≠ 0, y > 0 Answer: E Diff: 1 Var: 1 Section: 13.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

299

Calculus Early Transcendentals, 12e (Anton) Chapter 13 Partial Derivatives 13.2

Limits and Continuity

1) Evaluate

(3x + y).

A) 10 B) 7 C) 1 D) Does not exist E) 14 Answer: E Diff: 1 Var: 1 Section: 13.2 2) Evaluate

(2 + y) sin (πx).

A) 0 B) 1 C) 2 D) Does not exist E) 4 Answer: A Diff: 1 Var: 1 Section: 13.2 3) Evaluate

.

A) 133 B) 23 C) 101 D) Does not exist E) 8 Answer: A Diff: 1 Var: 1 Section: 13.2

300

4) Evaluate

(5x + 4y).

A) -14 B) 7 C) 1 D) Does not exist E) 34 Answer: E Diff: 1 Var: 1 Section: 13.2 5) Evaluate

.

A) 33 B) 26 C) -78 D) Does not exist E) 21 Answer: A Diff: 1 Var: 1 Section: 13.2 6) Evaluate

.

A) B) C) D) Does not exist E) Answer: E Diff: 1 Var: 1 Section: 13.2

301

7) Evaluate

.

A) B) C) D) Does not exist E) 12 Answer: A Diff: 1 Var: 1 Section: 13.2 8) Evaluate

.

A) -1944 B) 7004 C) -3567 D) Does not exist E) 42 Answer: A Diff: 1 Var: 1 Section: 13.2 9) Evaluate

.

A) 163,840 B) 7004 C) -3567 D) Does not exist E) 52 Answer: D Diff: 1 Var: 1 Section: 13.2

302

10) Evaluate

.

A) 6 B) 0.25 C) 3 D) Does not exist E) 5 Answer: B Diff: 1 Var: 1 Section: 13.2 11) Evaluate

(8x + 4y).

A) 60 B) 12 C) 44 D) 45 E) Does not exist Answer: A Diff: 1 Var: 1 Section: 13.2 12) Evaluate

.

A) 28 B) 14π C) 14 D) 7 E) Does not exist Answer: C Diff: 1 Var: 1 Section: 13.2 13) Evaluate

4(7x + 2y).

A) 176 B) 170 C) 200 D) 172 E) Does not exist Answer: C Diff: 1 Var: 1 Section: 13.2 303

14) Evaluate

.

A) 8 B) -1 C) 0 D) 1 E) 2 Answer: E Diff: 2 Var: 1 Section: 13.2 15) Determine whether the function f (x, y) =

has a removable discontinuity at the

origin.

A) (1, 0) B) (0, 1) C) (0, 0) D) (7, 0) E) (0, 7) Answer: C Diff: 3 Var: 1 Section: 13.2

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

304

Calculus Early Transcendentals, 12e (Anton) Chapter 14 Multiple Integrals 14.1

Double Integrals

1)

=

A) 10 B) 34 C) 11 D) 0 E) 16 Answer: D Diff: 1 Var: 1 Section: 14.1 2)

=

A) 18 B) 6 C) 0 D) 12 E) 5 Answer: B Diff: 2 Var: 1 Section: 14.1 3)

=

A) 12 B) 4 - 12 C) 12 D) 4 E) 2 Answer: A Diff: 2 Var: 1 Section: 14.1

305

4) Find the volume of the solid bounded by z = -2x - 2y and the rectangle A) 12 cubic units B) 25 cubic units C) 7 cubic units D) 144 cubic units E) 84 cubic units Answer: E Diff: 2 Var: 1 Section: 14.1 5) Find the volume of the solid bounded by z = 10 - 2x - 4y and the rectangle A) 32 cubic units B) 16 cubic units C) 8 cubic units D) 24 cubic units E) 128 cubic units Answer: B Diff: 2 Var: 1 Section: 14.1 6)

=

A) 10 B) 2 C) 0 D) -10 E) 20 Answer: E Diff: 2 Var: 1 Section: 14.1 7)

=

A) 11 B) 22 C) 0 D) -11 E) -22 Answer: B Diff: 2 Var: 1 Section: 14.1

306

8)

=

A) 39 B) 36 C) 33 D) 31 E) 38 Answer: B Diff: 1 Var: 1 Section: 14.1 9)

=

A) 14 B) 11 C) 8 D) 6 E) 13 Answer: B Diff: 1 Var: 1 Section: 14.1 10)

=

A) 0.341094 B) 0.001906 C) -0.234906 D) -0.501906 E) -0.001906 Answer: E Diff: 2 Var: 1 Section: 14.1 11)

=

A) 1.236641 B) 1.913641 C) 0.660641 D) 0.393641 E) 0.893641 Answer: E Diff: 2 Var: 1 Section: 14.1 307

12)

=

A) 3546 B) 3538 C) 3543 D) 3540 E) 3545 Answer: C Diff: 2 Var: 1 Section: 14.1

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

308

Calculus Early Transcendentals, 12e (Anton) Chapter 14 Multiple Integrals 14.2

Double Integrals over Nonrectangular Regions

1)

=

A) 4 B) 0 C) -4 D) π E) -π Answer: B Diff: 1 Var: 1 Section: 14.2 2)

=

A) 4 B) 20.25 C) 324 D) 40.5 E) 1.5 Answer: D Diff: 1 Var: 1 Section: 14.2

309

3)

=

A) 7 B) 7 C) 7 D) 7 E) Answer: E Diff: 1 Var: 1 Section: 14.2 4) Find the area of the region enclosed by y = -x and y = A) 5 B) C) D) 6 E) 0 Answer: B Diff: 3 Var: 1 Section: 14.2 5)

=

A) 32 B) 64 C) 128 D) 256 E) 0 Answer: B Diff: 2 Var: 1 Section: 14.2

310

, for -2 ≤ x ≤ -1.

6)

=

A) -16 B) 16 C) 8 D) -8 E) 0 Answer: A Diff: 1 Var: 1 Section: 14.2 7)

=

A) 14 B) 0 C) -14 D) -6.365 E) -20.365 Answer: E Diff: 2 Var: 1 Section: 14.2 8)

=

A) B) C) 0 D) E) 1 Answer: A Diff: 2 Var: 1 Section: 14.2

311

9) Find

where R is the region in the first quadrant enclosed between

and

A) B) 1 C) D) E) 0 Answer: D Diff: 2 Var: 1 Section: 14.2 10) Find

where R is the region in the first quadrant enclosed between

and x = 1.

A) B) C) D) E) 0 Answer: C Diff: 2 Var: 1 Section: 14.2

312

,

11) Find

by first interchanging the order of integration.

A) 1.322735 B) 1.822735 C) 2.322735 D) 2.168335 E) 0 Answer: B Diff: 2 Var: 1 Section: 14.2 12) Find the volume of the solid in the first octant bounded above by z = 16 and laterally by the circular cylinder A) 46.942899 B) 50.265482 C) 48.166899 D) 12.370021 E) 0 Answer: C Diff: 3 Var: 1 Section: 14.2

below by

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

313

314