test bank Preparation for Calculus, 1e Crauder, Evans, Noell test bank

Page 1

1. What is the domain of ?

ANSWER: a

2. What is the domain of ?

ANSWER: d

3. What is the domain of ?

ANSWER: c

4. What is the domain of ?

a. all real numbers except

b. all real numbers except

c. all real numbers except

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a. b.
c. d.
a. b. c.
d.
a. b. c. d.

Name: Class:

Chapter 1

d. all real numbers

ANSWER: b

5. If , compute

a. –15

b. –3

c. 0

d. 3

ANSWER: a

6. If , compute . a.

ANSWER: b

7. If , compute .

a. 0 b.

c. 6

d. undefined

ANSWER: b

8. If , compute . a.

Date:

ANSWER: d

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b. c. d.
b. c. d.

9. If , compute

b

10. If , compute , where . a. 1 b. 5

d. 5h ANSWER: b

11. If , then , where .

c

12. What is the range of ? a.

c

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a. b. c. d. ANSWER:
c.
a. b. 1 c. d. ANSWER:
b. c. d. ANSWER:

13. What is the range of ? a. b. c.

d.

ANSWER: d

14. Define h(x) by =

ANSWER: 2

15. Does this equation determine y as a function of x? Explain.

ANSWER: No. Observe that , so . So, for instance, the input x = 0 has two outputs, namely, y = 3 and y = –3. So, this equation cannot determine y as a function of x.

16. Does this equation determine y as a function of x? Explain.

ANSWER: Yes. Solve for y as follows:

Note that for any , there is exactly one output y. So, the equation determines y as a function of x.

17. Define j(x) by

ANSWER: 3

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Class: Date:
Name:
Chapter 1

18. If , then the average rate of change of f(x) over the interval [–2, 5] is

a. positive.

b. negative.

c. zero.

d. unable to be determined from this information.

ANSWER: b

19. Calculate the average rate of change for on the interval [–5, 20].

ANSWER: 5

20. Calculate the average rate of change for on the interval [0, 6].

ANSWER: 0

21. Calculate the average rate of change for on the interval [–8, 8].

ANSWER:

22. What are the units associated with the average rate of change for the function described in this scenario: H(z) is the length (in inches) of a corn stalk z days after it sprouts.

ANSWER: inches per day

23. What are the units associated with the average rate of change for the function described in this scenario: S(r) is the volume of a sphere (measured in cubic meters) whose radius r is measured in meters.

ANSWER: cubic meters per meter, or square meters

24. Compute the average rate of change of on the interval

ANSWER: c

25. Compute the average rate of change of on the interval [1, 1 + h]. a.

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Date:
Name: Class:
Chapter 1
a. 1 b. c. d.
m b. c.

ANSWER: b

26. Compute the average rate of change of on the interval [2, 2 + h].

ANSWER: d

27. If f(3) = f(4), what must be the average rate of change of f(x) on the interval [3, 4]?

ANSWER: 0

28. Refer to the graph here. On what interval(s) is this function increasing?

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Class: Date:
1
Name:
Chapter
d. a. b. c. d.

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Name: Class: Date: Chapter 1
7
a. b. c.

ANSWER: b

29. Refer to the graph here. On what interval is this function concave down?

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Name: Class: Date:
1
Chapter
8 d.
a.

ANSWER: a

30. Which of these statements about the graph is true?

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Class: Date: Chapter 1
Name:
b. c. d.

a. The function is decreasing on

b. The function has a local maximum at x = –2.

c. The local minimum of this function is 0.

d. The function is always concave up.

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10

ANSWER: b

31. Refer to the graph here. On which of these intervals is the average rate of change of this function positive?

ANSWER: d

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Date:
Name: Class:
Chapter 1
a. b. c. d.

32. Refer to the graph here. At which value of x does this function have a local minimum?

a. –0.8

b. –2

c. 0

d. 3

ANSWER: a

33. Refer to the graph here. On which interval(s) is the function decreasing?

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Class: Date:
Name:
Chapter 1

ANSWER:

34. Refer to the graph here. At what x-value(s) approximately does this function have a local minimum?

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Name: Class: Date: Chapter 1
13
a. b. c. d.
c

ANSWER: –1.2, 0.7

35. Refer to the graph here. What is the approximate absolute minimum of this function on the interval shown?

ANSWER: –9.2

36. Refer to the graph here. At what x-value(s) approximately does this function have a local maximum on the interval [–10, 5]?

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14

ANSWER: –9, –3, 4

37. Refer to the graph here. What is the approximate absolute maximum of this function on the interval [

10, 5]?

ANSWER: 10.5

38. Compute the limit: as a. 0 b. 1

d. ANSWER: a

39. Compute the limit: as

0 b. 1

ANSWER:

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Name: Class: Date: Chapter 1
c.
a.
c. d.
c

40. Compute the limit: as

a. 1

b. 0

c.

d.

ANSWER: d

41. Compute the limit: as

ANSWER:

42. Compute the limit: as

ANSWER: 0

43. Estimate the limit of f(x) as from the graph: a. 0

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Name: Class: Date:
Chapter 1

Chapter 1

b. 1

c. 60

d.

ANSWER: a

44. Use the fact that the limit of f(x) as is –3 to compute the limit as of .

a. 0

b.

c.

d.

ANSWER: c

45. Use the fact that the limit of f(x) as is 5 to compute the limit as of

ANSWER: –2

46. Use the fact that the limit of f(x) as is 8 to compute the limit as of

a.

b. 1

c. 0

d.

ANSWER: a

47. Compute the limit: as

c.

d.

ANSWER: d

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Name: Class: Date:
a. b.

48. Compute the limit: as

ANSWER: c

49. Compute the limit: as

ANSWER: d

50. Compute the limit: as

ANSWER: c

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Name: Class: Date: Chapter 1
a. b. c. 0 d.
a. b. c. 0 d.
a. b. c. d.

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test bank Preparation for Calculus, 1e Crauder, Evans, Noell test bank by nail basko - Issuu