Final Review - Calculus I

Name:

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Let

. Which of the following is true for

a.	0
b.	2
c.	3
d.	does not exist

Let

. Which of the following is true for

a.	–1
b.	0
c.
d.	does not exist

Which of the following is the best estimate of

a.	0
b.	0.667
c.	0.774
d.	1.50

Let

. Which of the following is true for

a.	–1
b.	0
c.	1
d.	2

Let

. Which of the following is true for

a.
b.	0
c.
d.	does not exist

Let

. Which of the following is true for

a.
b.
c.
d.	does not exist

Let

. Which of the following is true for

a.
b.
c.
d.	does not exist

a.	0
b.	2
c.	6
d.	12

Let

. Then

is continuous at 1 if

is redefined as?

a.
b.	1
c.	2
d.	3

10.

The largest set on which

is continuous is

a.
b.
c.
d.

11.

Which of the following correctly describes the discontinuities of

a.	is a jump discontinuity and is an infinite discontinuity.
b.	is a removable discontinuity and is a jump discontinuity.
c.	is a infinite discontinuity and is an removable discontinuity.
d.	is an removable discontinuity and is a infinite discontinuity.

12.

Which of the following is true for the limit

a.
b.
c.	0
d.	does not exist

13.

Which of the following is true for the limit

a.	–1
b.	0
c.	1
d.

14.

The limit

a.
b.	–2
c.	2
d.

15.

The limit

a.
b.	–2
c.	2
d.

16.

Let

. The set of all vertical asymptotes of

a.
b.
c.
d.

17.

Let

. The set of all horizontal asymptotes of

a.
b.
c.
d.

18.

A function

has horizontal asymptotes at

and

and a vertical asymptote at

. Which of the following statements about the limits of

could be true?

a.	, , and .
b.	, , and .
c.	, , and does not exist.
d.	, , and .

19.

The instantaneous rate of change of

a.
b.
c.
d.

20.

The derivative of

a.
b.
c.
d.

21.

h	0.1	0.01	0.001	–0.1	–0.01	–0.001
	–0.2381	–0.2488	–0.2499	–0.2632	–0.2513	–0.2501

What does the table above suggest about

a.
b.
c.
d.

22.

A ball thrown vertically from ground level returns to earth 6 seconds later. What is the ball’s maximum height in feet?

a.	48 ft
b.	96 ft
c.	144 ft
d.	576 ft

23.

Let

. Then

a.
b.
c.
d.

24.

Let

. Then

a.
b.
c.
d.

25.

Let

. Then

does not exist if

a.
b.
c.
d.	9

26.

Let

. Which of the following is true?

a.	does not have a derivative at 0
b.	has a corner at (0,0)
c.	has a horizontal tangent line at (0,0)
d.	has a vertical tangent line at (0,0)

27.

Let

. Which of the following is true?

a.	is discontinuous at 0
b.	does not have a derivative at 0
c.	has a horizontal tangent line at (0,0)
d.	has a vertical tangent line at (0,0)

28.

Let

. Then

a.
b.
c.	0
d.

29.

Let

. Then

when

a.
b.
c.	0
d.	1

30.

Let

. Then

for all

a.
b.
c.
d.

31.

Let

. Then

for all

a.
b.
c.
d.

32.

Let

. Then

a.
b.
c.
d.

33.

Let

. Then

a.
b.
c.
d.

34.

Let

. Then

a.
b.
c.
d.

35.

Let

. If

then

has a horizontal tangent line for each x in

a.
b.
c.
d.

36.

Let

. Then

a.
b.
c.
d.

37.

Let

. Then

a.
b.
c.
d.

38.

Let

. Which of the following is

a.
b.
c.
d.

39.

What is

a.	0
b.
c.
d.

40.

, then

a.
b.	1
c.
d.

41.

Let

Then

a.
b.
c.
d.

42.

Let

and

. By the chain rule,

a.
b.
c.
d.

43.

Let

. Then

a.
b.
c.
d.

44.

Let

. Then

a.
b.
c.
d.

45.

a.
b.
c.
d.

46.

a.
b.
c.
d.

47.

a.
b.
c.
d.

48.

Which of the following is the derivative of

with respect to x?

a.
b.
c.
d.

49.

a.
b.
c.
d.

50.

a.
b.
c.
d.

51.

When

a.
b.
c.
d.

52.

a.
b.
c.
d.

53.

a.
b.
c.
d.

54.

a.
b.
c.
d.

55.

a.
b.
c.
d.

56.

a.
b.
c.
d.

57.

a.
b.
c.
d.

58.

a.
b.
c.
d.

59.

The side length of a cubical game piece is measured at

cm and s is accurate to within 0.125 cm. What is the linear approximation of the maximum error in the surface area of the piece?

a.
b.
c.
d.

60.

Let

. If

when

, then

a.
b.
c.
d.

61.

Let

. If

when

, then

a.
b.
c.
d.

62.

Let

. If

and

when

and

, then

a.
b.
c.
d.

63.

If each edge of a cube is increasing at the rate of 3 cm/s when the length of an edge is 2 cm long, then the rate of increase of its volume is

a.
b.
c.
d.

64.

If the surface area of a sphere is shrinking at the rate of 0.1 sq cm/h when the radius is

cm, the rate of change of the radius is

a.
b.
c.
d.

65.

An isosceles triangle has equal sides 4 cm long and the included angle

. If

cm/min when

, then the rate of change of the area is

a.
b.
c.
d.

66.

A small rocket rising vertically is tracked by an observer located 25 km from the lift-off point. At a certain moment, the angle between the observer’s line of sight and the horizontal is

, and it is changing at rate of 0.25 radian per minute. How fast is the rocket rising at this moment?

a.	3.6084 km/min
b.	4.1667 km/min
c.	4.6875 km/min
d.	8.3333 km/min

67.

Let

. The set of all critical numbers of

a.
b.
c.
d.

68.

Let

. The absolute minimum and maximum of

are located respectively at

a.
b.
c.
d.

69.

Let

. The absolute minimum and maximum of

are located respectively at

a.
b.
c.
d.

70.

Let

. The absolute minimum and maximum of

are located respectively at

a.
b.
c.
d.

71.

What are all the critical points of

a.
b.
c.
d.	, , and

72.

What is the minimum value of

on the interval

a.	0
b.	70
c.
d.	6

73.

The function

represents the concentration of a medication (in

) in a patient’s bloodstream after t hours. What is the maximum concentration in the time interval

a.
b.
c.
d.

74.

Let

. Then the set of all

guaranteed by the Mean Value Theorem is

a.
b.
c.
d.

75.

Let

. Then the set of all

guaranteed by the Mean Value Theorem is

a.
b.
c.
d.

76.

The largest set on which the function

is increasing is

a.
b.
c.
d.

77.

Let

. Then

has a relative minimum at

a.
b.
c.
d.

78.

Let

. Then

has a relative maximum at

a.
b.
c.
d.

79.

Let

. Then

has a relative maximum at

a.
b.
c.
d.

80.

Let

. Then

has a point of inflection at

a.
b.
c.
d.

81.

Let

. Then

has a point of inflection at

a.
b.
c.
d.

82.

Let

. Then

has a point of inflection at

a.
b.
c.
d.

83.

Which of the following statements about the function given by

is true?

a.	The graph of the function has one point of inflection and the function has two relative extrema.
b.	The graph of the function has two points of inflection and the function has one relative extremum.
c.	The graph of the function has two points of inflection and the function has two relative extrema.
d.	The graph of the function has three points of inflection and the function has two relative extrema.

84.

Let

. What does the Second Derivative Test establish about the behavior of

at its single critical point?

a.	There is a point of inflection at the critical point.
b.	There is a local minimum at the critical point.
c.	There is a local maximum at the critical point.
d.	Nothing; the Second Derivative Test fails.

85.

Determine which of the following is true for the limit

a.
b.
c.
d.

86.

Determine which of the following is true for the limit

a.
b.
c.
d.

87.

Determine which of the following is true for the limit

a.
b.
c.
d.

88.

Determine which of the following is true for the limit

a.
b.
c.
d.

89.

Determine which of the following is not true for the graph of

a.	is continuous on
b.	has a relative minimum at
c.	has a point of inflection at
d.	is concave upward on

90.

Determine which of the following is not true for the graph of

a.	has a relative maximum at
b.	has a relative minimum at
c.	has points of inflection at
d.	is concave downward on

91.

Determine which of the following is not true for the graph of

a.	has an oblique asymptote:
b.	has a vertical asymptote:
c.	has a jump discontinuity at:
d.	has no horizontal asymptote

92.

Suppose that, when a stone is thrown upwards with a speed of 60 miles an hour, its height,

feet, after

seconds, is given by

. The maximum height of the stone is

a.	120
b.	121
c.	125
d.	200

93.

The antiderivative of

a.
b.
c.
d.

94.

The antiderivative of

a.
b.
c.
d.

95.

The antiderivative of

a.
b.
c.
d.

96.

The particular solution of the differential equation

satisfying the initial conditions

and

a.
b.
c.
d.

97.

Let

and

. Which of the following equations satisfies these conditions?

a.
b.
c.
d.

98.

Let A denote the area enclosed by the graph

, the x-axis, and the lines

and

. Graphing the region and using plane geometry, we can find that A is

a.
b.
c.
d.

99.

Let A denote the area enclosed by the graph

,the x-axis, and the lines

and

. Graphing the region and using plane geometry, we can find that A is

a.
b.
c.
d.

100.

Suppose

is the upper sum of the area enclosed by the graph

the x-axis, and the lines

and

by partitioning

into four subintervals

, and

. Then

a.	26
b.	28
c.	48
d.	60

101.

The value of the definite integral

a.
b.
c.	2
d.	4

102.

, then

a.
b.
c.
d.	impossible to find with the given information

103.

Graph of f

The graph of the piecewise-defined function f is shown in the figure above. What is

a.
b.
c.
d.	9

104.

a.	0
b.	8
c.	16
d.	20

105.

The derivative

a.
b.
c.
d.

106.

By part 2 of the Fundamental Theorem of Calculus ,

a.
b.
c.
d.

107.

Let

, and

, then

a.
b.
c.	38
d.	60

108.

The bounds m and M used in the Bounds on an Integral Theorem for

are

a.
b.
c.
d.

109.

The average value of

a.
b.
c.
d.

110.

The antiderivative

a.
b.
c.
d.

111.

The antiderivative

a.
b.
c.
d.

112.

The antiderivative

a.
b.
c.
d.

113.

The indefinite integral

a.
b.
c.
d.

114.

The indefinite integral

a.
b.
c.
d.

115.

a.
b.
c.
d.

116.

The differential equation

describes the change in velocity of a skydiver in freefall in meters per second. If the initial velocity of the skydiver is 0 m/s, which function models the skydiver’s velocity over time?