Calculus for Scientists and Engineers 1st Edition Briggs Test Bank by a185794639

Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the average velocity of the function over the given interval. 1) y = x2 + 6x, [6, 9] A) 21 2) y = 3x3 - 8x2 + 6, [-8, 5] 181 A) 13

B) 15

C) 45

D) 7

B) 171

2223 C) 5

181 D) 5

C) 2

3 D) 10

3) y =

2x, [2, 8] 1 A) 3

4) y =

3) B) 7

3 , [4, 7] x-2

1 3

5) y = 4x2 , 0,

B) -

3 10

C) 2

D) 7

7 4

A) 2

1 3

C) -

3 10

D) 7

6) y = -3x2 - x, [5, 6] A) -34

7) h(t) = sin (4t), 0, A)

B) -

4 π

1 6

C) -2

1 2

π 8

8 π

8) g(t) = 3 + tan t, -

7) B) -

8 π

π 8

4 π

π π , 4 4

8) B) -

8 5

C) 0

D) -

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4 π

Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Use the table to find the instantaneous velocity of y at the specified value of x. 9) x = 1. x y 0 0 0.2 0.02 0.4 0.08 0.6 0.18 0.8 0.32 1.0 0.5 1.2 0.72 1.4 0.98 A) 2

B) 0.5

C) 1

D) 1.5

10) x = 1. x y 0 0 0.2 0.01 0.4 0.04 0.6 0.09 0.8 0.16 1.0 0.25 1.2 0.36 1.4 0.49 A) 1

10)

B) 0.5

C) 1.5

D) 2

11) x = 1. x y 0 0 0.2 0.12 0.4 0.48 0.6 1.08 0.8 1.92 1.0 3 1.2 4.32 1.4 5.88 A) 4

11)

B) 2

C) 6

D) 8

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 12) x = 2. x y 0 10 0.5 38 1.0 58 1.5 70 2.0 74 2.5 70 3.0 58 3.5 38 4.0 10 A) 4

12)

B) 8

C) 0

D) -8

13) x = 1. x y 0.900 -0.05263 0.990 -0.00503 0.999 -0.0005 1.000 0.0000 1.001 0.0005 1.010 0.00498 1.100 0.04762 A) 0

13)

B) -0.5

C) 1

D) 0.5

C) slope is -39

1 D) slope is 20

Find the slope of the curve for the given value of x. 14) y = x2 + 5x, x = 4 4 A) slope is 25 15) y = x2 + 11x - 15, x = 1 4 A) slope is 25 16) y = x3 - 5x, x = 1 A) slope is -3

14)

B) slope is 13

15) 1 B) slope is 20

C) slope is 13

D) slope is -39

16) B) slope is 1

C) slope is 3

D) slope is -2

17) y = x3 - 3x2 + 4, x = 1 A) slope is 0

B) slope is --3

C) slope is -3

D) slope is 1

18) y = 2 - x3 , x = 1 A) slope is 0

B) slope is -3

C) slope is -1

D) slope is 3

17)

18)

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Solve the problem. 19) Given lim f(x) = Ll, lim f(x) = Lr, and Ll ≠ Lr, which of the following statements is true? x→0 x→0 + I.

lim f(x) = Ll x→0

II.

lim f(x) = Lr x→0

19)

III. lim f(x) does not exist. x→0 A) I 20) Given

B) none

C) II

D) III

lim f(x) = Ll, lim f(x) = Lr , and Ll = Lr, which of the following statements is false? x→0 x→0 +

lim f(x) = Ll x→0

II.

lim f(x) = Lr x→0

20)

III. lim f(x) does not exist. x→0 A) I

B) II

C) III

D) none

21) If lim f(x) = L, which of the following expressions are true? x→0 I.

lim f(x) does not exist. x→0 -

II.

lim f(x) does not exist. x→0 +

III.

lim f(x) = L x→0 -

IV.

lim f(x) = L x→0 +

A) II and III only

B) III and IV only

C) I and II only

21)

D) I and IV only

22) What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a? A) Either the limit of f(x) as x→a from the left exists or the limit of f(x) as x→a from the right exists B) The limit of f(x) as x→a from the left exists, the limit of f(x) as x→a from the right exists, and at least one of these limits is the same as f(a). C) f(a) exists, the limit of f(x) as x→a from the left exists, and the limit of f(x) as x→a from the right exists. D) The limit of f(x) as x→a from the left exists, the limit of f(x) as x→a from the right exists, and these two limits are the same.

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22)

Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Use the graph to evaluate the limit. 23) lim f(x) x→-1

23)

-6 -5 -4 -3 -2 -1

B) -

3 4

6 x

-1

A) -1

C) ∞

3 4

24) lim f(x) x→0

24) y 4 3 2 1

-4

-3

-2

-1

4 x

-1 -2 -3 -4

A) does not exist

C) -3

B) 3

D) 0

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 25) lim f(x) xâ&#x2020;&#x2019;0

25) 6

5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1

6 x

-2 -3 -4 -5 -6

A) does not exist

B) 3

C) 0

D) -3

26) lim f(x) xâ&#x2020;&#x2019;0

26)

10 8 6 4 2 -2

-1

-2 -4

A) does not exist

C) -1

B) 0

D) 6

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 27) lim f(x) x→0

27)

y 4 3 2 1 -4

-3

-2

-1

4 x

-1 -2 -3 -4

A) 1

C) -1

B) does not exist

D) ∞

28) lim f(x) x→0

28)

y 4 3 2 1 -4

-3

-2

-1

4 x

-1 -2 -3 -4

A) does not exist

B) -1

C) ∞

D) 1

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 29) lim f(x) xâ&#x2020;&#x2019;0

29) y 4 3 2 1

-4

-3

-2

-1

-1 -2 -3 -4

A) 2

B) 0

C) does not exist

D) -2

30) lim f(x) xâ&#x2020;&#x2019;0

30) y 4 3 2 1

-4

-3

-2

-1

-1 -2 -3 -4

A) 0

B) does not exist

C) 1

D) -2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 31) lim f(x) x→0

31) y 4 3 2 1

-4

-3

-2

-1

-1 -2 -3 -4

A) -2 32) Find

B) does not exist

C) 2

D) -1

lim f(x) and lim f(x) x→(-1)x→(-1)+

32)

y 2

-4

-2

-4

-6

A) -7; -2

B) -2; -7

C) -7; -5

D) -5; -2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Use the table of values of f to estimate the limit. 33) Let f(x) = x2 + 8x - 2, find lim f(x). x→2 x f(x)

1.9

1.99

1.999

33)

2.001

2.01

2.1

A) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = ∞ f(x) 5.043 5.364 5.396 5.404 5.436 5.763 B) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 5.40 f(x) 5.043 5.364 5.396 5.404 5.436 5.763 C) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 18.0 f(x) 16.810 17.880 17.988 18.012 18.120 19.210 D) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 17.70 f(x) 16.692 17.592 17.689 17.710 17.808 18.789 34) Let f(x) =

x f(x)

x-4 , find lim f(x). x-2 x→4 3.9

3.99

3.999

34)

4.001

4.01

4.1

A) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 5.10 f(x) 5.07736 5.09775 5.09978 5.10022 5.10225 5.12236 B) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 1.20 f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745 C) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 4.0 f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485 D) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = ∞ f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 35) Let f(x) = x2 - 5, find lim f(x). x→0 -0.1

x f(x)

-0.01

35)

-0.001

0.001

0.01

0.1

A) x -0.1 f(x) -1.4970

-0.01 -1.4999

-0.001 -1.5000

0.001 0.01 0.1 ; limit = -15.0 -1.5000 -1.4999 -1.4970

x -0.1 f(x) -1.4970

-0.01 -1.4999

-0.001 -1.5000

0.001 0.01 0.1 ; limit = ∞ -1.5000 -1.4999 -1.4970

x -0.1 f(x) -2.9910

-0.01 -2.9999

-0.001 -3.0000

0.001 0.01 0.1 ; limit = -3.0 -3.0000 -2.9999 -2.9910

x -0.1 f(x) -4.9900

-0.01 -4.9999

-0.001 -5.0000

0.001 0.01 0.1 ; limit = -5.0 -5.0000 -4.9999 -4.9900

36) Let f(x) =

x f(x)

x-3 x2 + 2x - 15

, find lim f(x). x→3

2.9

2.99

2.999

36)

3.001

3.01

3.1

A) x 2.9 2.99 2.999 3.001 3.01 3.1 ; limit = 0.125 f(x) 0.1266 0.1252 0.1250 0.1250 0.1248 0.1235 B) x 2.9 2.99 2.999 3.001 3.01 3.1 ; limit = -0.125 f(x) -0.1266 -0.1252 -0.1250 -0.1250 -0.1248 -0.1235 C) x 2.9 2.99 2.999 3.001 3.01 3.1 ; limit = 0.025 f(x) 0.0266 0.0252 0.0250 0.0250 0.0248 0.0235 D) x 2.9 2.99 2.999 3.001 3.01 3.1 ; limit = 0.225 f(x) 0.2266 0.2252 0.2250 0.2250 0.2248 0.2235

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 37) Let f(x) =

x f(x)

x2 - 5x + 4 , find lim f(x). x2 - 6x + 5 x→1 0.9

0.99

37)

0.999

1.001

1.01

1.1

A) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.75 f(x) 0.7561 0.7506 0.7501 0.7499 0.7494 0.7436 B) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.65 f(x) 0.6561 0.6506 0.6501 0.6499 0.6494 0.6436 C) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.8333 f(x) 0.8361 0.8336 0.8334 0.8333 0.8331 0.8305 D) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.85 f(x) 0.8561 0.8506 0.8501 0.8499 0.8494 0.8436 38) Let f(x) =

x f(x)

sin(6x) , find lim f(x). x x→0

-0.1

-0.01 5.99640065

-0.001

38)

0.001

0.01 5.99640065

A) limit = 6 C) limit = 5.5 39) Let f(θ) =

0.1

B) limit does not exist D) limit = 0

cos (6θ) , find lim f(θ). θ θ→0

x -0.1 f(θ) -8.2533561

-0.01

-0.001

39)

0.001

0.01

0.1 8.2533561

B) limit = 6 D) limit = 8.2533561

A) limit does not exist C) limit = 0

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 40) It can be shown that the inequalities 1 -

x2 x sin(x) < < 1 hold for all values of x close 6 2 - 2 cos(x)

to zero. What, if anything, does this tell you about

x sin(x) ? Explain. 2 - 2 cos(x)

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40)

Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 41) Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" and include a statement of any restrictions on the principle. lim g(x) x→a g(x) M A) If lim g(x) = M and lim f(x) = L, then lim = = , provided that f(x) lim f(x) L x→a x→a x→a x→a

41)

f(a) ≠ 0. lim g(x) x→a g(x) M B) If lim g(x) = M and lim f(x) = L, then lim = = , provided that lim f(x) L x→a x→a x→a f(x) x→a L ≠ 0. g(x) g(a) C) lim . = f(a) x→a f(x) g(x) g(a) D) lim , provided that f(a) ≠ 0. = f(a) x→a f(x) 42) Provide a short sentence that summarizes the general limit principle given by the formal notation lim [f(x) ± g(x)] = lim f(x) ± lim g(x) = L ± M, given that lim f(x) = L and lim g(x) = M. x→a x→a x→a x→a x→a

42)

A) The sum or the difference of two functions is the sum of two limits. B) The limit of a sum or a difference is the sum or the difference of the functions. C) The limit of a sum or a difference is the sum or the difference of the limits. D) The sum or the difference of two functions is continuous. 43) The statement "the limit of a constant times a function is the constant times the limit" follows from a combination of two fundamental limit principles. What are they? A) The limit of a product is the product of the limits, and a constant is continuous. B) The limit of a product is the product of the limits, and the limit of a quotient is the quotient of the limits. C) The limit of a constant is the constant, and the limit of a product is the product of the limits. D) The limit of a function is a constant times a limit, and the limit of a constant is the constant. Find the limit. 44) lim x→7

A) 7

44) B)

D) 10

45) lim (9x - 4) x→1 A) -5 46)

45) B) -13

C) 5

D) 13

lim (15 - 2x) x→-18 A) 21

43)

46) B) -21

C) 51

D) -51

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Give an appropriate answer. 47) Let lim f(x) = 5 and lim g(x) = -8. Find lim [f(x) - g(x)]. x→9 x→9 x→9 A) 9 48) Let

B) 13

B) -4

C) -36

48) D) 4

f(x) lim f(x) = 9 and lim g(x) = -4. Find lim . g(x) x → -9 x → -9 x → -9

A) -

50) Let

D) -3

lim f(x) = -9 and lim g(x) = 4. Find lim [f(x) ∙ g(x)]. x → -4 x → -4 x → -4

A) -5

49) Let

C) 5

47)

4 9

B) -9

lim f(x) = 16. Find lim x → -2 x → -2

A) 2.0000

C) 13

49) D) -

9 4

f(x).

50)

B) -2

C) 4

D) 16

51) Let lim f(x) = 1 and lim g(x) = -7. Find lim [f(x) + g(x)]2 . x→1 x→1 x→1 A) 50

B) -6

52) Let lim f(x) = 243. Find lim x→6 x→6 A) 3

C) 8

52)

B) 6

14 3

D) 36

f(x). C) 5

53) Let lim f(x) = -8 and lim g(x) = 6. Find lim x→ 1 x→ 1 x→ 1 A) -

51)

D) 243

6f(x) - 10g(x) . -9 + g(x)

B) 1

C) 36

53) D) - 4

Find the limit. 54) lim (x3 + 5x2 - 7x + 1) x→2 A) 0 55)

B) does not exist

C) 29

D) 15

lim (3x5 - 3x4 - 4x3 + x2 + 5) x→-2 A) -7

56)

54)

55)

B) -167

C) 41

D) -103

x lim 3x +2 x→-1 A) 1

56) B) -

1 5

C) 0

D) does not exist

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 57) lim x→0

x3 - 6x + 8 x-2

A) -4

57) B) 0

C) Does not exist

D) 4

3x2 + 7x - 2 58) lim x→1 3x2 - 4x - 2 A) Does not exist

59)

58) B) -

7 4

C) 0

D) -

8 3

lim (x + 3)2 (x - 1)3 x→-2 A) -675

60) lim x→7

B) -1

C) -27

D) -25

x2 + 4x + 4

A) 81 61) lim x→5

59)

60) B) ±9

C) 9

D) does not exist

7x + 51

A) -86

62) lim h→0

61) B)

C) - 86

D) 86

2 3h + 4 + 2

A) 1

63) lim x→0 A) 1/2

62) B) 2

C) 1/2

D) Does not exist

1+x-1 x

63) B) Does not exist

C) 1/4

D) 0

Determine the limit by sketching an appropriate graph. for x < 1 64) lim f(x), where f(x) = -3x + 4 5x 5 for x ≥ 1 + x → 1A) 1 65)

66)

B) 6

lim f(x), where f(x) = -2x + 2 4x + 3 x → 6+ A) -10

C) 5

D) 10

for x < 6 for x ≥ 6

65)

B) 4

2 lim f(x), where f(x) = x + 4 0 x → 4+ A) 0

64)

C) 27

D) 3

for x ≠ 4 for x = 4

66)

B) 12

C) 16

D) 20

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67)

lim f(x), where f(x) = x → 1A) 4

68)

lim f(x), where f(x) = x → -7 + A) Does not exist

1 - x2 1 4 B) 1 x 1 0 B) -7

0≤x<1 1≤x<4 x=4

67) C) 0

D) Does not exist

-7 ≤ x < 0, or 0 < x ≤ 1 x=0 x < -7 or x > 1 C) -0

68) D) 6

Find the limit, if it exists. x3 + 12x2 - 5x 69) lim 5x x→0 A) -1

69) B) 0

C) Does not exist

D) 5

x4 - 1 70) lim x→1 x - 1 A) 0

71)

B) 2

lim x → -5

lim x→7

lim x→2

B) 4

C) 2

D) 1

72) B) 2

C) 120

D) 12

73) B) 3

C) 17

D) Does not exist

x2 + 2x - 8 x2 - 4

A) Does not exist

75)

71)

x2 + 3x - 70 x-7

A) 0

74)

D) 4

x2 + 12x + 35 x+5

A) Does not exist

73)

C) Does not exist

x2 - 4 lim x→2 x-2 A) Does not exist

72)

70)

74) B) 0

3 2

D) -

1 2

x2 - 4 lim 2 x → 2 x - 7x + 10 A) -

4 3

75) C) -

B) 0

2 3

D) Does not exist

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank x2 - 9x + 18 76) lim x→6 x2 - 3x - 18

76) B) -

A) 1

77)

lim h→0

lim x → 10

1 3

D) Does not exist

(x + h)3 - x3 h

A) 0

78)

1 3

77) C) 3x2 + 3xh + h2

B) Does not exist

D) 3x2

10 - x 10 - x

78)

A) Does not exist

C) -1

B) 0

D) 1

Provide an appropriate response. 79) It can be shown that the inequalities -x ≤ x cos

1 ≤ x hold for all values of x ≥ 0. x

79)

1 Find lim x cos if it exists. x x→0 A) 0.0007

80) The inequality 1Find lim x→0 A) 1

B) 0

C) does not exist

D) 1

x2 sin x < < 1 holds when x is measured in radians and x < 1. 2 x

sin x if it exists. x B) 0.0007

C) does not exist

D) 0

81) If x3 ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists. x→0 A) -1

80)

B) 1

81) C) does not exist

D) 0

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Compute the values of f(x) and use them to determine the indicated limit. 82) If f(x) = x2 + 8x - 2, find lim f(x). x→2 x f(x)

1.9

1.99

1.999

2.001

2.01

82)

2.1

A) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = ∞ f(x) 5.043 5.364 5.396 5.404 5.436 5.763 B) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 18.0 f(x) 16.810 17.880 17.988 18.012 18.120 19.210 C) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 17.70 f(x) 16.692 17.592 17.689 17.710 17.808 18.789 D) x 1.9 1.99 1.999 2.001 2.01 2.1 ; limit = 5.40 f(x) 5.043 5.364 5.396 5.404 5.436 5.763

83) If f(x) =

x f(x)

x4 - 1 , find lim f(x). x-1 x→1 0.9

0.99

83)

0.999

1.001

1.01

1.1

A) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 4.0 f(x) 3.439 3.940 3.994 4.006 4.060 4.641 B) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 5.10 f(x) 4.595 5.046 5.095 5.105 5.154 5.677 C) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 1.210 f(x) 1.032 1.182 1.198 1.201 1.218 1.392 D) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = ∞ f(x) 1.032 1.182 1.198 1.201 1.218 1.392

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 84) If f(x) =

x3 - 6x + 8 , find lim f(x). x-2 x→0 -0.1

x f(x)

-0.01

-0.001

84)

0.001

0.01

0.1

A) x -0.1 0.001 0.01 0.1 -0.01 -0.001 ; limit = -1.20 f(x) -1.22843 -1.20298 -1.20030 -1.19970 -1.19699 -1.16858 B) x -0.1 0.001 0.01 0.1 -0.01 -0.001 ; limit = ∞ f(x) -1.22843 -1.20298 -1.20030 -1.19970 -1.19699 -1.16858 C) x -0.1 0.001 0.01 0.1 -0.01 -0.001 ; limit = -2.10 f(x) -2.18529 -2.10895 -2.10090 -2.99910 -2.09096 -2.00574 D) x -0.1 0.001 0.01 0.1 -0.01 -0.001 ; limit = -4.0 f(x) -4.09476 -4.00995 -4.00100 -3.99900 -3.98995 -3.89526 85) If f(x) =

x f(x)

x-4 , find lim f(x). x-2 x→4 3.9

3.99

3.999

85)

4.001

4.01

4.1

A) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 5.10 f(x) 5.07736 5.09775 5.09978 5.10022 5.10225 5.12236 B) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = ∞ f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745 C) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 4.0 f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485 D) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 1.20 f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 86) If f(x) = x2 - 5, find

-0.1

x f(x)

lim f(x). x→0

86)

-0.01

-0.001

0.001

0.01

0.1

A) x -0.1 f(x) -1.4970

-0.01 -1.4999

-0.001 -1.5000

0.001 0.01 0.1 ; limit = -15.0 -1.5000 -1.4999 -1.4970

x -0.1 f(x) -4.9900

-0.01 -4.9999

-0.001 -5.0000

0.001 0.01 0.1 ; limit = -5.0 -5.0000 -4.9999 -4.9900

x -0.1 f(x) -1.4970

-0.01 -1.4999

-0.001 -1.5000

0.001 0.01 0.1 ; limit = ∞ -1.5000 -1.4999 -1.4970

x -0.1 f(x) -2.9910

-0.01 -2.9999

-0.001 -3.0000

0.001 0.01 0.1 ; limit = -3.0 -3.0000 -2.9999 -2.9910

87) If f(x) =

x f(x)

x+1 , find lim f(x). x+1 x→1 0.9

0.99

87)

0.999

1.001

1.01

1.1

A) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.21213 f(x) 0.21764 0.21266 0.21219 0.21208 0.21160 0.20702 B) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 0.7071 f(x) 0.72548 0.70888 0.70728 0.70693 0.70535 0.69007 C) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = 2.13640 f(x) 2.15293 2.13799 2.13656 2.13624 2.13481 2.12106 D) x 0.9 0.99 0.999 1.001 1.01 1.1 ; limit = ∞ f(x) 0.21764 0.21266 0.21219 0.21208 0.21160 0.20702

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 88) If f(x) =

x f(x)

x - 2, find

3.9

lim f(x). x→4

3.99

88)

3.999

4.001

4.01

4.1

A) x 3.9 f(x) 3.9000

3.99 2.9000

3.999 1.9000

4.001 4.01 4.1 ; limit = ∞ 2.0000 3.0000 4.0000

B) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 0 f(x) -0.02516 -0.00250 -0.00025 0.00025 0.00250 0.02485 C) x 3.9 3.99 3.999 4.001 4.01 4.1 ; limit = 1.50 f(x) 1.47736 1.49775 1.49977 1.50022 1.50225 1.52236 D) x 3.9 f(x) 3.9000

3.99 2.9000

3.999 1.9000

4.001 4.01 4.1 ; limit = 1.95 2.0000 3.0000 4.0000

For the function f whose graph is given, determine the limit. 89) Find lim f(x) and lim f(x). x→-1 x→-1 +

89)

y 4 2 -6

-4

-2

6 x

-2 -4 -6 -8 -10

A) -5; -2

B) -7; -2

C) -7; -5

D) -2; -7

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 90) Find

lim f(x) and x→2 -

lim f(x). x→2 +

90)

y 8 6 4 2 -4

-3

-2

-1

-2 -4 -6 -8

A) 1; 1 C) -2; 4

B) does not exist; does not exist D) 4; -2

91) Find lim f(x). x→2 -

91)

f(x) 8 7 6 5 4 3 2 1 -2

-1

A) -1

B) 2.3

C) 1.3

D) 4

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 92) Find lim f(x). xâ&#x2020;&#x2019;1 -

92) 5

f(x)

4 3 2 1 -5

-4

-3

-2

-1

5 x

-1 -2 -3 -4 -5

1 2

B) does not exist

C) 2

D) -1

93) Find lim f(x). xâ&#x2020;&#x2019;1 +

93) 5

f(x)

4 3 2 1 -5

-4

-3

-2

-1

5 x

-1 -2 -3 -4 -5

A) 3

B) 3

1 2

C) 4

D) does not exist

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 94) Find lim f(x). x→0

94) 5

4 3 2 1 -5

-4

-3

-2

-1

5 x

-1 -2 -3 -4 -5

A) -3

B) does not exist

C) 0

D) 3

95) Find lim f(x). x→0

95) 5

4 3 2 1 -5

-4

-3

-2

-1

5 x

-1 -2 -3 -4 -5

A) -1

B) 0

C) does not exist

D) 1

96) Find lim f(x). x→0

96)

8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8

A) -4

1 2 3 4 5 6 7 8 x

B) 0

C) 4

D) does not exist

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 97) Find lim f(x). x→-1

97) y 4

2 A -4

-2

-4

1 2

B) -

C) -1

D) does not exist

98) Find lim f(x). x→-∞

98) 5

f(x)

4 3 2 1 -5

-4

-3

-2

-1

5 x

-1 -2 -3 -4 -5

A) 0

C) -2

B) does not exist

D) -∞

Find the limit. 99)

1 lim x→-2 x + 2 A) Does not exist

100)

B) -∞

C) ∞

D) 1/2

1 lim x +4 x → -4 A) -∞

101)

99)

100) B) -1

C) 0

D) ∞

1 lim 2 x → 10+ (x - 10) A) 0

101) B) ∞

C) -∞

D) -1

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 102)

6 lim 2 x -4 x → -2 A) -∞

103)

B) ∞

C) 1

D) ∞

lim tan x x→(π/2)+

104) C) -∞

B) 0

D) 1

lim sec x x→(-π/2)A) -∞

106)

D) -1 103)

B) -∞

A) ∞ 105)

C) 0

1 lim 2 x → 3+ x - 9 A) 0

104)

102)

105) B) 0

C) 1

D) ∞

lim (1 + csc x) x→0+

106) B) ∞

A) 1

C) 0

D) Does not exist

107) lim (1 - cot x) x→0 A) -∞

108)

lim x → -3 -

lim x → 3+

C) ∞

B) 0

D) Does not exist

x2 - 7x + 12 x3 - 9x

108) B) ∞

A) 0

109)

107)

C) -∞

D) Does not exist

x2 - 4x + 3 x3 - x

A) -∞

109) B) 0

C) Does not exist

D) ∞

Find all vertical asymptotes of the given function. 4x 110) g(x) = x-6 A) none 111) f(x) =

110)

B) x = 4

C) x = -6

D) x = 6

x+9 x2 - 49

111)

A) x = 49, x = -9 C) x = 0, x = 49

B) x = -7, x = 7 D) x = -7, x = 7, x = -9

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 112) g(x) =

x+3

112)

x2 + 49

A) x = -7, x = 7 C) x = -7, x = 7, x = -3 113) h(x) =

B) none D) x = -7, x = -3

x + 11

113)

x2 + 64x

A) x = 0, x = -8, x = 8 C) x = 0, x = -64 114) f(x) =

B) x = -8, x = 8 D) x = -64, x = -11

x(x - 1)

114)

x3 + 16x

A) x = 0 C) x = -4, x = 4

115) R(x) =

B) x = 0, x = -4, x = 4 D) x = 0, x = -16

-3x2 2 x + 4x - 77

115)

A) x = - 77 C) x = 11, x = -7 116) R(x) =

B) x = -11, x = 7, x = -3 D) x = -11, x = 7

x-1 3 x + 8x2 - 33x

116)

A) x = -3, x = 0, x = 11 C) x = -11, x = 0, x = 3 117) f(x) =

-2x(x + 2) 4x2 - 3x - 7

A) x = -

118) f(x) =

B) x = -11, x = 3 D) x = -3, x = -30, x = 11

7 ,x=1 4

117) B) x = -

4 ,x=1 7

C) x =

D) x =

7 , x = -1 4

x-3 9x - x3

118)

A) x = 0, x = 3 C) x = -3, x = 3

119) f(x) =

4 , x = -1 7

B) x = 0, x = -3 D) x = 0, x = -3, x = 3

-x2 + 16 x2 + 5x + 4

A) x = -1

119) B) x = 1, x = -4

C) x = -1, x = 4

D) x = -1, x = -4

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Choose the graph that represents the given function without using a graphing utility. x 120) f(x) = x-1 A)

120)

B) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

8 10

D) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 121) f(x) =

121)

x2 + x + 3

B) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

8 10

D) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 122) f(x) =

x2 - 2 x3

122)

B) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

8 10

D) y

-10 -8 -6 -4 -2

8 10

-10 -8 -6 -4 -2

-2

-4

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 123) f(x) =

1 x+1

123)

B) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

10 x

D) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 124) f(x) =

x-1 x+1

124)

B) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

10 x

D) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 125) f(x) =

125)

(x + 2)2

B) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

10 x

D) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 126) f(x) =

2x2

126)

4 - x2

B) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

10 x

D) 10

-10 -8

-6

-4

-2

10 x

-10 -8

-6

-4

-2

-4

-6

-8

-10

Find the limit. 127)

9 lim -1 x→∞ x A) -1

128)

B) -10

C) 1

D) 8

3 lim x→-∞ 6 - (1/x2 ) A) 3

129)

127)

128) B)

1 2

C) -∞

3 5

-6 + (2/x) lim x→-∞ 6 - (1/x2 ) A) -∞

129) B) ∞

C) 1

D) - 1

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 130)

x2 + 5x + 3 lim x→∞ x3 - 8x2 + 13 A) ∞

131)

B) 0

1 7

7 11

17 12

D) ∞

132) C) ∞

B) 0

3 4

9x3 - 5x2 + 3x lim x→∞ -x3 - 2x + 5

133) B) ∞

3 2

D) 9

5x3 + 2x2 lim x→ - ∞ x - 7x2 A) ∞

135)

D) 1

6x + 1 lim x→∞ 8x - 7

A) -9

134)

3 13

131) B)

A) -

133)

-17x2 + 5x + 7 lim x→-∞ -12x2 - 4x + 11 A) 1

132)

130)

134) B) -∞

C) 5

D) -

2 7

cos 5x x

lim x→-∞ A) 5

135) C) -∞

B) 0

D) 1

Divide numerator and denominator by the highest power of x in the denominator to find the limit. 4x2 136) lim x→∞ 5 + 49x2 A)

137)

2 7

lim x→∞ A) 0

C) does not exist

4 5

49x2 + x - 3 (x - 15)(x + 1)

lim x→∞ A) ∞

138)

4 49

136)

137) B) 7

C) 49

D) 0

-4 x + x-1 2x - 3

138) B) ∞

1 2

D) - 2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 139)

-4x-1 + 2x-3 lim x→∞ -4x-2 + x-5

139) B) ∞

A) 0

C) 1

D) -∞

140)

x - 7x - 4 lim x→-∞ -6x + x2/3 - 2 A)

6 7

B) 0

7 6

D) -∞

81t2 - 729 t-9

141) lim t→∞ A) 81

141) B) does not exist

C) 729

D) 9

25t2 - 125 t-5

142) lim t→∞

A) does not exist

143)

140)

142) B) 25

C) 125

D) 5

3x + 7 7x2 + 1

lim x→∞ A) ∞

143) B)

3 7

C) 0

Find all horizontal asymptotes of the given function, if any. 5x - 8 144) h(x) = x-4 A) y = 0 C) y = 5 145) h(x) = 8 -

3 x

145) B) y = 3 D) no horizontal asymptotes

x2 + 5x - 8 x-8

146)

A) y = 0 C) y = 8

147) h(x) =

144) B) y = 4 D) no horizontal asymptotes

A) x = 0 C) y = 8

146) g(x) =

B) y = 1 D) no horizontal asymptotes

8x2 - 5x - 8 2x2 - 4x + 2

147)

A) y = 0 C) y =

3 7

B) y = 4

5 4

D) no horizontal asymptotes

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 148) h(x) =

8x4 - 5x2 - 9 5x5 - 4x + 9

A) y =

148)

8 5

B) y =

C) y = 0

149) h(x) =

D) no horizontal asymptotes

2x3 - 7x 8x3 - 3x + 8

A) y =

149)

7 3

B) y =

C) y = 0

150) h(x) =

8x3 - 7x - 6 9x2 + 7

C) y =

150) B) y = 0

8 9

D) no horizontal asymptotes

4x + 1 x2 - 36

151) B) y = 4 D) y = 0

A) no horizontal asymptotes C) y = -6, y = 6

152) R(x) =

-3x2 + 1 2 x + 3x - 40

152)

A) y = -8, y = 5 C) y = 0

153) f(x) =

B) y = -3 D) no horizontal asymptotes

x2 - 5

153)

25x - x4

A) y = -5, y = 5 C) no horizontal asymptotes

154) f(x) =

1 4

D) no horizontal asymptotes

A) y = 8

151) h(x) =

5 4

B) y = 0 D) y = -1

49x4 + x2 - 7 x - x3

154)

A) y = -49 C) no horizontal asymptotes

B) y = 0 D) y = -1, y = 1

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Sketch the graph of a function y = f(x) that satisfies the given conditions. 155) f(0) = 0, f(1) = 3, f(-1) = -3, lim f(x) = -2, lim f(x) = 2. x→-∞ x→∞

155)

156) f(0) = 0, f(1) = 4, f(-1) = 4,

lim f(x) = -4. x→±∞

156)

157) f(0) = 4, f(1) = -4, f(-1) = -4,

lim f(x) = 0. x→±∞

157)

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 158) f(0) = 0,

lim f(x) = 0, lim f(x) = -∞, lim f(x) = -∞, lim f(x) = ∞, x→±∞ x→3 x→-3+ x→3 +

158)

lim f(x) = ∞. x→-3 y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all points where the function is discontinuous. 159)

A) None

159)

B) x = 4

C) x = 4, x = 2

D) x = 2

160)

A) None

B) x = -2, x = 1

C) x = -2

D) x = 1

161)

A) x = 0, x = 2 C) x = -2, x = 0

B) x = -2, x = 0, x = 2 D) x = 2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 162)

162)

A) x = 6

C) x = -2, x = 6

B) None

D) x = -2

163)

A) x = 1, x = 5 C) None

B) x = 4 D) x = 1, x = 4, x = 5

164)

A) None

B) x = 1

C) x = 0

D) x = 0, x = 1

165)

A) x = 0

B) x = 0, x = 3

C) None

D) x = 3

166)

A) x = -2

B) x = -2, x = 2

C) None

D) x = 2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 167)

167)

A) x = -2, x = 0, x = 2 C) x = 0

B) None D) x = -2, x = 2

Provide an appropriate response. 168) Is f continuous at f(1)? -x2 + 1, 2x, f(x) = -4, -2x + 4 3,

168) 6

-1 â&#x2030;¤ x < 0 0<x<1 x=1 1<x<3 3<x<5

5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1

-2 -3 -4 -5

(1, -4)

-6

A) Yes

B) No

169) Is f continuous at f(0)? -x2 + 1, -1 â&#x2030;¤ x < 0 3x, 0<x<1 f(x) = -4, x=1 -3x + 6 1 < x < 3 1, 3<x<5

169) 6

5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1

-2 -3 -4 -5

(1, -4)

-6

A) No

B) Yes

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 170) Is f continuous at x = 0?

170) 10

x3 , f(x) = -2x, 7, 0,

-2 < x ≤ 0 0≤x<2 2<x≤4 x=2

8 6 4 2 (2, 0) -5

-4

-3

-2

-1

5 t

-2 -4 -6 -8 -10

A) Yes

B) No

171) Is f continuous at x = 4?

171) 10

x3 , f(x) = -4x, 4, 0,

-2 < x ≤ 0 0≤x<2 2<x≤4 x=2

8 6 4 2 (2, 0) -5

-4

-3

-2

-1

5 t

-2 -4 -6 -8 -10

A) Yes

B) No

Find the intervals on which the function is continuous. 3 172) y = - 5x x+1

172)

A) discontinuous only when x = -6 C) discontinuous only when x = -1 173) y =

B) discontinuous only when x = 1 D) continuous everywhere

173)

(x + 2)2 + 4 B) discontinuous only when x = -16 D) discontinuous only when x = 8

A) continuous everywhere C) discontinuous only when x = -2 174) y =

x+2 2 x - 15x + 56

174)

A) discontinuous only when x = 7 or x = 8 C) discontinuous only when x = 7

B) discontinuous only when x = -8 or x = 7 D) discontinuous only when x = -7 or x = 8

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 175) y =

175)

x2 - 9

A) discontinuous only when x = 9 C) discontinuous only when x = -3 or x = 3

176) y =

B) discontinuous only when x = -3 D) discontinuous only when x = -9 or x = 9

3 x2 x +4 8

176)

A) discontinuous only when x = -4 C) discontinuous only when x = -12 177) y =

B) continuous everywhere D) discontinuous only when x = -8 or x = -4

sin (4θ) 3θ

177)

A) discontinuous only when θ =

π 2

B) discontinuous only when θ = 0

C) discontinuous only when θ = π

178) y =

D) continuous everywhere

4 cos θ θ+1

178)

A) discontinuous only when θ = -1 C) discontinuous only when θ =

B) continuous everywhere

π 2

D) discontinuous only when θ = 1

179) y = 8x + 8 A) continuous on the interval - 1, ∞ C) continuous on the interval 1, ∞

180) y =

179) B) continuous on the interval - 1, ∞ D) continuous on the interval -∞, - 1

7x - 8

180)

8 A) continuous on the interval -∞, 7 C) continuous on the interval

8 B) continuous on the interval , ∞ 7

8 ,∞ 7

D) continuous on the interval -

181) y = x2 - 3 A) continuous on the interval [- 3, 3] B) continuous on the intervals (-∞, - 3] and [ 3, ∞) C) continuous everywhere D) continuous on the interval [ 3, ∞)

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8 ,∞ 7

181)

Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank Provide an appropriate response. 182) Is f continuous on (-2, 4]?

182) 10

x3 ,

-2 < x ≤ 0 0≤x<2 2<x≤4 x=2

f(x) = -4x, 3, 0,

8 6 4 2 (2, 0) -5

-4

-3

-2

-1

5 t

-2 -4 -6 -8 -10

A) No

B) Yes

Find the limit, if it exists. 183)

lim (x2 - 16 + x→-3

x2 - 36)

A) -10

B) -4

A) 11

D) ±11

C) -2.6457513

B) Does not exist

D) 0 186)

B) ± 187

A) 8 5

lim x→2+

185)

187

D) Does not exist

x2 - 64

lim x→-8 -

187) B) 4

C) 0

D) Does not exist

4 (x - 2)3 x-2

A) 0

188) B) 4

C) 4 2

D) Does not exist

(t + 36)(t - 1)2 13t - 13

lim t→1 + A)

C) Does not exist

x2 - 9

lim x→14

A) 93.5

189)

184) B) 121

A) 2.64575131

188)

D) 4

x - 10

185) lim x→3

187)

C) Does not exist

x2 + 14x + 49

184) lim x→4

186)

183)

1 13

189)

37 13

C) 0

D) Does not exist

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 190) Use the Intermediate Value Theorem to prove that 7x3 + 9x2 - 6x - 5 = 0 has a solution

190)

between -2 and -1. 191) Use the Intermediate Value Theorem to prove that -2x4 - 5x3 - 3x - 9 = 0 has a solution

191)

between -2 and -1. 192) Use the Intermediate Value Theorem to prove that x(x - 2)2 = 2 has a solution between 1 and 3. 193) Use the Intermediate Value Theorem to prove that 4 sin x = x has a solution between

π 2

192)

193)

and π. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find numbers a and b, or k, so that f is continuous at every point. 194) x<2 -10, f(x) = ax + b, 2 ≤ x ≤ 4 2, x>4 A) a = 6, b = -22 B) a = -10, b = 2 C) a = 6, b = 26

194)

D) Impossible

195)

195) x2 ,

x < -1 f(x) = ax + b, -1 ≤ x ≤ 3 x + 6, x > 3 A) a = -2, b = 3

B) a = 2, b = -3

C) a = 2, b = 3

D) Impossible

196)

196) 3x + 4, if x < -8 f(x) = kx + 2, if x ≥ -8 1 A) k = 4

B) k = -

1 4

C) k =

11 4

D) k = 5

197)

197) x2 ,

if x ≤ 4

f(x) = x + k, if x > 4 A) k = -4

B) k = 12

C) k = 20

D) Impossible

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 198)

198) x2 , if x ≤ 9 f(x) = kx, if x > 9 1 A) k = 9

B) k = 9

C) k = 81

Solve the problem. 199) Select the correct statement for the definition of the limit:

D) Impossible

lim f(x) = L x→x0

199)

means that __________________ A) if given a number ε > 0, there exists a number δ > 0, such that for all x, 0 < x - x0 < δ implies f(x) - L > ε. B) if given any number ε > 0, there exists a number δ > 0, such that for all x, 0 < x - x0 < δ implies f(x) - L < ε. C) if given any number ε > 0, there exists a number δ > 0, such that for all x, 0 < x - x0 < ε implies f(x) - L > δ. D) if given any number ε > 0, there exists a number δ > 0, such that for all x, 0 < x - x0 < ε implies f(x) - L < δ. 200) Identify the incorrect statements about limits. I. The number L is the limit of f(x) as x approaches x0 if f(x) gets closer to L as x approaches x0 .

200)

II. The number L is the limit of f(x) as x approaches x0 if, for any ε > 0, there corresponds a δ > 0 such that f(x) - L < ε whenever 0 < x - x0 < δ. III. The number L is the limit of f(x) as x approaches x0 if, given any ε > 0, there exists a value of x for which f(x) - L < ε. A) I and III

B) II and III

C) I and II

D) I, II, and III

Use the graph to find a δ > 0 such that for all x, 0 < x - x 0 < δ ⇒ f(x) - L < ε. 201)

201) y

y=x+2

f(x) = x + 2 x0 = 2

4.2

L=4 ε = 0.2

4 3.8

1.8 2 2.2 NOT TO SCALE

A) 0.1

B) 2

C) 0.4

D) 0.2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 202)

202) y

y = 4x - 2 f(x) = 4x - 2 x0 = 2

6.2 6

L=6 ε = 0.2

5.8

2 

1.95

2.05

NOT TO SCALE A) 0.1

B) 0.05

C) 0.5

D) 4

203)

203) y

y = -4x - 1 3.2 f(x) = -4x - 1 x0 = -1

L=3 ε = 0.2

2.8

 -1  -1.05

-0.95

NOT TO SCALE A) -0.05

B) 6

C) 0.5

D) 0.05

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 204)

204) y

y = -x + 2 4.2

f(x) = -x + 2 x0 = -2

L=4 ε = 0.2

3.8

-2.2 -2 -1.8

NOT TO SCALE B) -0.2

A) 0.4

C) 0.2

D) 6

205)

205) y

3 x+3 2

6.2 f(x) = 6

x0 = 2 L=6 ε = 0.2

5.8

3 x+3 2

1.9 2 2.1 NOT TO SCALE

A) -0.2

B) 4

C) 0.1

D) 0.2

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 206)

206) y =-

4 x+1 3

3.9

4 f(x) = - x + 1 3

3.7

x0 = -2 L = 3.7 ε = 0.2

3.5

-2.2

-2

-1.9

NOT TO SCALE A) -0.3

B) 5.7

C) 0.1

D) 0.3

207)

207) y

f(x) = x x0 = 3 L= y=

1 ε= 4

1.98 1.73 1.48

2.1975

3.9275

NOT TO SCALE A) 0.9275

B) 0.8025

C) 1.73

D) -1.27

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 208)

208) y

f(x) = x - 3 x0 = 4

L=1 1 ε= 4

x-3

1.25 1 0.75 0

3.5625 4

4.5625

NOT TO SCALE A) 0.5625

B) 1

C) 0.4375

D) 3

209)

209) y

y = x2 5

f(x) = x2 x0 = 2

L=4 ε=1

 2  1.73

2.24

NOT TO SCALE A) 2

B) 0.27

C) 0.24

D) 0.51

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 210)

210) y

y = x2 - 1 f(x) = x2 - 1 x0 = 3

9 8

L=8 ε=1

3 

2.83

3.16

NOT TO SCALE A) 0.16

B) 5

C) 0.33

D) 0.17

A function f(x), a point x 0 , the limit of f(x) as x approaches x 0 , and a positive number ε is given. Find a number δ > 0 such that for all x, 0 < x - x 0 < δ ⇒ f(x) - L < ε. 211) f(x) = 9x + 3, L = 21, x0 = 2, and ε = 0.01 A) 0.005556

211)

B) 0.002222

C) 0.001111

D) 0.005

C) 0.001667

D) 0.003333

C) 0.004

D) -0.01

212) f(x) = 3x - 10, L = -4, x0 = 2, and ε = 0.01 A) 0.005

212)

B) 0.006667

213) f(x) = -10x + 9, L = -1, x0 = 1, and ε = 0.01 A) 0.002

213)

B) 0.001

214) f(x) = -9x - 6, L = -33, x0 = 3, and ε = 0.01 A) -0.003333

214)

B) 0.001111

C) 0.002222

D) 0.000556

215) f(x) = 3x2, L =12, x0 = 2, and ε = 0.2 A) 1.98326

215)

B) 2.0166

C) 0.01674

D) 0.0166

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prove the limit statement 216) lim (3x - 2) = 7 x→3

216)

x2 - 64 217) lim = 16 x→8 x - 8

218) lim x→9

217)

2x2 - 15x- 27 = 21 x-9

218)

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Full file at https://testbankuniv.eu/Calculus-for-Scientists-and-Engineers-1st-Edition-Briggs-Test-Bank 1 1 219) lim = xâ&#x2020;&#x2019;9 x 9

219)

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Answer Key Testname: UNTITLED1

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39)

A B A B D A A A C B C C D B C D C B D C B D D A C B B A D D A B C C D A A A A

x2 40) Answers may vary. One possibility: lim 1 = lim 1 = 1. According to the squeeze theorem, the function 6 x→0 x→0 x sin(x) x2 , which is squeezed between 1 and 1, must also approach 1 as x approaches 0. Thus, 2 - 2 cos(x) 6 x sin(x) lim = 1. 2 2 cos(x) x→0 41) B 42) C 43) C 53

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Answer Key Testname: UNTITLED1

44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 78) 79) 80) 81) 82) 83) 84) 85) 86) 87) 88) 89) 90) 91) 92) 93)

C C C B C D C D A C D D A A D C C B C A A C D C B A D B B C C A C D A B A D B A D C B B B D D C C A 54

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Answer Key Testname: UNTITLED1

94) 95) 96) 97) 98) 99) 100) 101) 102) 103) 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) 114) 115) 116) 117) 118) 119) 120) 121) 122) 123) 124) 125) 126) 127) 128) 129) 130) 131) 132) 133) 134) 135) 136) 137) 138) 139) 140) 141) 142) 143)

B B D A C A A B B D C D B D C B D B B C A D C D B A D C C A C C D A B D B C D A A B A B A B C D D B 55

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Answer Key Testname: UNTITLED1

144) 145) 146) 147) 148) 149) 150) 151) 152) 153) 154) 155)

C C D B C B D D B B C Answers may vary. One possible answer: 8

6 4 2 -8

-6

-4

-2

8 x

-2 -4 -6 -8

156) Answers may vary. One possible answer: 8

6 4 2 -8

-6

-4

-2

8 x

-2 -4 -6 -8

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Answer Key Testname: UNTITLED1

157) Answers may vary. One possible answer: y 12 10 8 6 4 2 -12 -10 -8 -6 -4 -2-2 -4 -6

4 6 8 10 12 x

-8 -10 -12

158) Answers may vary. One possible answer: y 2

-8

-6

-4

-2

8 x

-2

159) 160) 161) 162) 163) 164) 165) 166) 167) 168) 169) 170) 171) 172) 173) 174) 175) 176) 177) 178) 179)

B D B A C A D B C B A A A C A A C B B A A 57

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Answer Key Testname: UNTITLED1

180) 181) 182) 183) 184) 185) 186) 187) 188) 189)

C B A A A B C C A B

190) Let f(x) = 7x3 + 9x2 - 6x - 5 and let y0 = 0. f(-2) = -13 and f(-1) = 3. Since f is continuous on [-2, -1] and since y0 = 0 is between f(-2) and f(-1), by the Intermediate Value Theorem, there exists a c in the interval (-2 , -1) with the property that f(c) = 0. Such a c is a solution to the equation 7x3 + 9x2 - 6x - 5 = 0. 191) Let f(x) = -2x4 - 5x3 - 3x - 9 and let y0 = 0. f(-2) = 5 and f(-1) = -3. Since f is continuous on [-2, -1] and since y0 = 0 is between f(-2) and f(-1), by the Intermediate Value Theorem, there exists a c in the interval (-2, -1) with the property that f(c) = 0. Such a c is a solution to the equation -2x4 - 5x3 - 3x - 9 = 0. 192) Let f(x) = x(x - 2)2 and let y0 = 2. f(1) = 1 and f(3) = 3. Since f is continuous on [1, 3] and since y0 = 2 is between f(1) and f(3), by the Intermediate Value Theorem, there exists a c in the interval (1, 3) with the property that f(c) = 2. Such a c is a solution to the equation x(x - 2)2 = 2. 193) Let f(x) = f

π π and f(π), by the Intermediate Value Theorem, there exists a c in the interval , π , with the property that 2 2

f(c) = 194) 195) 196) 197) 198) 199) 200) 201) 202) 203) 204) 205) 206) 207) 208) 209) 210) 211) 212) 213) 214) 215)

sin x 1 π π 1 and let y0 = . f , π and since y0 = is between ≈ 0.6366 and f(π) = 0. Since f is continuous on x 4 2 2 4

1 . Such a c is a solution to the equation 4 sin x = x. 4

A C C B B B A D B D C C C B C C A C D B B D 58

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Answer Key Testname: UNTITLED1

216) Let ε > 0 be given. Choose δ = ε/3. Then 0 < x - 3 < δ implies that (3x - 2) - 7 = 3x - 9 = 3(x - 3) = 3 x - 3 < 3δ = ε Thus, 0 < x - 3 < δ implies that (3x - 2) - 7 < ε 217) Let ε > 0 be given. Choose δ = ε. Then 0 < x - 8 < δ implies that x2 - 64 (x - 8)(x + 8) - 16 = - 16 x-8 x-8 for x ≠ 8 = (x + 8) - 16 = x -8 < δ=ε x2 - 64 Thus, 0 < x - 8 < δ implies that - 16 < ε x-8 218) Let ε > 0 be given. Choose δ = ε/2. Then 0 < x - 9 < δ implies that 2x2 - 15x- 27 (x - 9)(2x + 3) - 21 = - 21 x-9 x-9 for x ≠ 9 = (2x + 3) - 21 = 2x - 18 = 2(x - 9) = 2 x - 9 < 2δ = ε 2x2 - 15x- 27 Thus, 0 < x - 9 < δ implies that - 21 < ε x-9 219) Let ε > 0 be given. Choose δ = min{9/2, 81ε/2}. Then 0 < x - 9 < δ implies that 1 1 9-x = x 9 9x =

1 1 ∙ ∙ x-9 x 9

1 1 81ε ∙ ∙ =ε 9/2 9 2

Thus, 0 < x - 9 < δ implies that

1 1 <ε x 9

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