Test Bank for Calculus Early Transcendentals Multivariable, 11th Edition Howard Anton, Irl C. Bivens

Test Bank for Calculus Early Transcendentals Multivariable, 11th Edition Howard Anton, Irl C. Bivens, Stephen Davis Chapter 11-15 Chapter 11 11.1

Three-dimensional Space; Vectors

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

+

+

1

is

Answer: D Diff: 1 Var: 1 Section: 11.1

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

2

E) 4 + 4 = 1 Answer: A Diff: 2 Var: 1 Section: 11.1 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)

+

+

= 66 3

E) Answer: C Diff: 2 Var: 1 Section: 11.1

+

= 66

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

4

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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> 5

= (-5, 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

6

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

7

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

8

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

9

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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Calculus Early Transcendentals, 12e (Anton) 10

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

11

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

12

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

13

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

14

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

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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 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

16

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).

17

(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

18

(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

>

19

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

20

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

21

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

© (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.

22

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

23

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

24

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

25

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.

26

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

27

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

28

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

29

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 30

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.

31

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

32

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

33

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 34

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.

35

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

36

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

37

, 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

38

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

39

,

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.

40

Calculus Early Transcendentals, 12e (Anton) Chapter 15 Topics in Vector Calculus 15.1

Vector Fields

1) F(x, y, z) = xyzi + 6yj + xk. Find div F. A) yz + 6 B) yz - 1 C) xy - 6 - xz D) xy - 6 + xz E) yz - 6 Answer: A Diff: 1 Var: 1 Section: 15.1 2) F(x, y, z) = 9 i + (2y - 6)j + 3k. Find div F. A) 18x + 2 B) 36x C) 18x D) 18x + 5 E) 36x + 5 Answer: A Diff: 1 Var: 1 Section: 15.1 3) F(x, y, z) = (4xy - 9)i + 8xyzj + A) 0 B) 4xy + 8xyz + C) 4y + 8xz + 2z D) 2z E) 4xy + Answer: C Diff: 1 Var: 1 Section: 15.1

k. Find div F.

4) F(x, y, z) = (12xy - 12)i + 4xyzj + ( A) 12y + 4xz + 2z B) 12xy + 4xyz + z2 C) 0 D) 2z E) 12xy + z2 Answer: A Diff: 1 Var: 1 Section: 15.1

- 12)k. Find div F.

41

5) F(x, y, z) = 4xyi + 8xyzj + ( A) 0 B) 4xy + 8xyz + 8x C) 4y + 8xz + 2z − 8x D) 2z E) 4xy + z2 Answer: C Diff: 1 Var: 1 Section: 15.1

- 8zx)k. Find div F.

6) F(x, y, z) = xyzi + (y - 3)j + (z + 3)k. Find curl F. A) xzi B) xzi - zj C) xyj - xzk D) xyj + xzk E) xzi + zj Answer: C Diff: 1 Var: 1 Section: 15.1 7) Let F(x, y, z) = i+ A) 2 +5 +5 B) 2 C)

i+5 j+5 + +

D) E) 2

j+

k. Find div F.

j+

k. Find curl F.

k

+5 +

+5

Answer: A Diff: 1 Var: 1 Section: 15.1 8) Let F(x, y, z) = i+ A) 5 +5 +2 B) 5 i + 5 j + 2 k C) + + D) 0 E) 12 Answer: D Diff: 1 Var: 1 Section: 15.1

42

9) Let F(x, y, z) =

i+

A) 3

+

+4

B) 3

+

+ 4y

C) 3

i+

j+4

D) E) 3

jy

k. Find div F.

jy

k. Find curl F.

k

+ 4y +

+4

Answer: B Diff: 2 Var: 1 Section: 15.1 10) Let F(x, y, z) =

i+

A) 3

+

+4

B) 3

+

+ 4y

C)

i+

D) E) 3

k + 4y

+

+ 4y

Answer: C Diff: 2 Var: 1 Section: 15.1

43

11) Let F(x, y, z) = y i + cos(xy)j + xz A) 0 B) 4yz + x cos(xy) + x(1 + 3z) C) 4yz - x sin(xy) + x(1 + 3z) D) 4yz i + x cos(xy)j + x(1 + 3z) k E) 4y cos(xy)(z + 3 ) Answer: C Diff: 3 Var: 1 Section: 15.1

k. Find div F.

12) Let F(x, y, z) = y i + sin(xyz)j + xz k. Find curl F. A) (5xy - z )i + xy cos(xyz)j + (yz cos(xyz) )k B) (5xy - z )i + (yz cos(xyz) )j + xy cos(xyz)k C) 0 D) xy cos(xyz)i + (5xy - z )j + (yz cos(xyz) )k E) xy cos(xyz) + 5xy - z ) + (yz cos(xyz) ) Answer: D Diff: 3 Var: 1 Section: 15.1 13) Which vector field could be illustrated by the graph shown?

A) 3i + 6j B) 6i + 3j C) 3i - 6j D) 6i - 3j E) 3i - 3j Answer: C Diff: 3 Var: 1 Section: 15.1

44

14) Which vector field could be illustrated by the graph shown?

A) -3xi B) 3j C) 3yi D) -3yj E) 3xi Answer: A Diff: 3 Var: 1 Section: 15.1 15) Which vector field could be illustrated by the graph shown?

A) F(x, y) = 3i B) F(x, y) = 3yi C) F(x, y) = 3xj D) F(x, y) = 3yj E) F(x, y) = 3xi Answer: E Diff: 3 Var: 1 Section: 15.1

45

16) Which vector field could be illustrated by the graph shown?

A) F(x, y) = 5xi + 5yj B) F(x, y) = 5yi + 5xj C) F(x, y) = 5i + 5j D) F(x, y) = 5i - 5j E) F(x, y) = -5i - 5yj Answer: C Diff: 3 Var: 1 Section: 15.1

© (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.

Calculus Early Transcendentals, 12e (Anton) 46

Chapter 15 15.2

Topics in Vector Calculus

Line Integrals

1)

where x = t and y = 3t, (0 ≤ t ≤ 1), is

A) B) C) D) E) Answer: E Diff: 1 Var: 1 Section: 15.2 2)

where x = t and y = 3t, (0 ≤ t ≤ 1), is

A) B) C) D) E) Answer: B Diff: 1 Var: 1 Section: 15.2

47

3)

where x = t and y = 3t, (0 ≤ t ≤ 1), is

A) B) C) D) E) Answer: D Diff: 1 Var: 1 Section: 15.2 4)

where x = 2t, y = t, and z = −2t, (0 ≤ t ≤ 1), is

A) B) 4 C) 0 D) E) -4 Answer: E Diff: 2 Var: 1 Section: 15.2 5)

where x = -t, y = 2t, and z = 2t, (0 ≤ t ≤ 1), is

A) -9 B) 9 C) 6 D) -6 E) 0 Answer: B Diff: 2 Var: 1 Section: 15.2 48

where x = 2t, y = t, and z = −2t, (0 ≤ t ≤ 1), is

6) A) -6 B) 6 C) 4 D) -4 E) 0 Answer: A Diff: 2 Var: 1 Section: 15.2 7)

along the curve x =

from (0, 0) to (1, 1) is

A) B) 0 C) -2 D) -7 E) Answer: A Diff: 3 Var: 1 Section: 15.2 8)

x = sin t, y = cos t, (0 ≤ t ≤ π), is

A) 0 B) 3 C) 6 D) 12 E) 24 Answer: A Diff: 2 Var: 1 Section: 15.2

49

9) The work done by F(x, y) = 3xi + 3xyj along the curve x = y2 from (0, 0) to (1, 1) is A) 2.25 B) 4.5 C) 3 D) 6 E) 0 Answer: A Diff: 1 Var: 1 Section: 15.2 10) The work done by F(x, y) = 10xi + 21xyj along the curve y = A) 28 B) 14 C) 42 D) -14 E) 17 Answer: B Diff: 1 Var: 1 Section: 15.2

from (0, 0) to (1, 1) is

11) The work done by F(x, y) = 3 i + 3 j along the curve x = A) 4 B) 2 C) 6 D) -2 E) 5 Answer: B Diff: 1 Var: 1 Section: 15.2

from (0, 0) to (1, 1) is

12) The work done by the force F(x, y) = 12 i + 24 j acting on a particle that moves along the circle x = cos t, y = sin t, from (1, 0) to (0, 1).

A) 48 B) 24 C) 4 D) -36 E) 36 Answer: C Diff: 3 Var: 1 Section: 15.2 © (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.

50

51