Chapter 6

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Chapter 6

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

Select the correct answer.

a.
b.
c.
d.
e.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

Select the correct answer.

a.
b.
c.
d.
e.

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

Find the average value of the function on the given interval.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

Find the derivative of the function.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Select the correct answer.

a.
b.
c.
d.
e.

Use logarithmic differentiation to find the derivative of the function.

Select the correct answer.

a.
b.
c.
d.
e.

10.

Find the limit.

Select the correct answer.

a.	1
b.	0
c.
d.
e.

11.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.

12.

Find the volume of the solid obtained by rotating about the y axis the region bounded by the curves.

Select the correct answer.

a.
b.
c.
d.
e.

13.

Calculate g(x), where

. State the domain and range of g. Calculate

Select the correct answer.

a.
b.
c.
d.
e.

14.

Express the quantity as a single logarithm.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

15.

Use the properties of logarithms to expand the quantity.

Select the correct answer.

a.
b.
c.
d.
e.

16.

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

17.

Find the limit.

Select the correct answer.

a.
b.	3
c.	0
d.
e.

18.

At what point of the curve

does the tangent line have slope 4?

Select the correct answer.

a.
b.
c.
d.
e.

19.

Find an equation of the tangent line to the curve

at the point

.

Select the correct answer.

a.
b.
c.
d.
e.

20.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.

21.

Find

Select the correct answer.

a.
b.
c.
d.
e.

22.

Find the limit.

Select the correct answer.

a.	4
b.	0
c.
d.
e.

23.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.

24.

Find the limit.

Select the correct answer.

a.	6
b.
c.	0
d.
e.

25.

Use l'Hospital's Rule to calculate the exact value of the limit as

Select the correct answer.

a.
b.
c.
d.	0
e.

26.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

Select the correct answer.

a.	3.14134
b.	3.66016
c.	7.32031
d.	7.38905
e.	none of these

27.

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

28.

Find

Select the correct answer.

a.
b.
c.
d.
e.	none of these

29.

For the period from 1980 to 2000, the percentage of households in the United States with at least one VCR has been modeled by the function

where the time t is measured in years since midyear 1980,

Use derivatives to estimate the time at which the number of VCRs was increasing most rapidly.

Select the correct answer.

a.
b.
c.
d.
e.

30.

The geologist C. F. Richter defined the magnitude of an earthquake to be

where I is the intensity of the quake (measured by the amplitude of a seismograph 100 km from the epicenter) and S is the intensity of a ”standard” earthquake (where the amplitude is only

cm). The 1989 Loma Prieta earthquake that shook San Francisco had a magnitude of 7.1 on the Richter scale. The 1906 San Francisco earthquake was 16 times as intense. What was its magnitude on the Richter scale?

Select the correct answer.

a.	113.6
b.	8.3
c.	8.5
d.	8.4
e.	124

31.

Use logarithmic differentiation to find the derivative of the function.

Select the correct answer.

a.
b.
c.
d.
e.

32.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.

33.

Find the derivative of y.

Select the correct answer.

a.
b.
c.
d.
e.

34.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

Select the correct answer.

a.	3.66016
b.	3.14134
c.	7.38905
d.	10.98047
e.	7.38915

35.

Select the correct answer.

a.
b.
c.
d.
e.

36.

Find the limit.

Select the correct answer.

a.	0
b.	1
c.
d.
e.

37.

A painting in an art gallery has height h and is hung so that lower edge is a distance d above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle

subtended at his eye by the painting?)

Select the correct answer.

a.
b.
c.
d.
e.

38.

A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes six revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Select the correct answer.

a.
b.
c.
d.
e.

39.

Use the definitions of the hyperbolic functions to find the following limit.

Select the correct answer.

a.	0
b.
c.	1
d.
e.

40.

Find

Select the correct answer.

a.
b.
c.
d.
e.

41.

A telephone line hangs between two poles at 12 m apart in the shape of the catenary

, where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

Select the correct answer.

a.	0.1203
b.	0.8962
c.	0.4888
d.	0.8079
e.	0.1389

42.

Find the limit.

Select the correct answer.

a.
b.	2
c.	0
d.
e.

43.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.
f.	none of these

44.

Find the limit.

Select the correct answer.

a.	0
b.
c.
d.
e.

45.

Find the average value of the function on the given interval.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

46.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.

47.

Evaluate the integral to three decimal places.

Select the correct answer.

a.	0.194
b.	0.533
c.	0.183
d.	0.583
e.	0.094

48.

Find the average value of the function on the given interval.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

49.

Select the correct answer.

a.	23
b.	22
c.	26
d.	25
e.	28

50.

Suppose that the graph of

is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 2 ft.

Select the correct answer.

a.	66.99 mi
b.	409.37 mi
c.	202.56 mi
d.	264.79 mi
e.	609.99 mi

51.

Solve the inequality.

Select the correct answer.

a.
b.
c.
d.
e.

52.

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

53.

Use logarithmic differentiation to find the derivative of the function.

Select the correct answer.

a.
b.
c.
d.
e.

54.

Find the limit.

Select the correct answer.

a.	0
b.	1
c.
d.
e.

55.

Find

Select the correct answer.

a.
b.
c.
d.
e.

56.

Evaluate the integral.

Select the correct answer.

a.
b.
c.
d.
e.	none of these

57.

If f is a one-to-one function such that f(6) = 1, what is

Select the correct answer.

a.	5
b.	2
c.	6
d.	3
e.	7
f.	11

58.

Determine f(x) from the table. The values from the table are given to the nearest ten thousandth.

Select the correct answer.

a.
b.
c.
d.
e.

59.

Find the inverse of the function.

Select the correct answer.

a.
b.
c.
d.
e.

60.

Differentiate the function.

Select the correct answer.

a.
b.
c.
d.
e.

61.

Find the average value of the function on the given interval.

Select the correct answer.

a.
b.
c.
d.
e.

Numeric Response

62.

Use the properties of logarithms to expand the quantity.

__________

63.

Find the solution of the equation correct to four decimal places.

__________

64.

Suppose that the graph of

is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft. Give the answer to two decimal places.

__________

65.

Use logarithmic differentiation to find the derivative of the function.

__________

66.

If a bacteria population starts with 50 bacteria and doubles every three hours, then the number of bacteria after t hours is

. When will the population reach 60,000?

__________

67.

Differentiate the function.

__________

68.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

__________

69.

Differentiate the function.

__________

70.

Evaluate the integral.

__________

71.

Find

__________

72.

Solve each equation for x.

___________

73.

Evaluate the integral.

__________

74.

Use logarithmic differentiation to find the derivative of the function.

__________

75.

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

___________

76.

Find

__________

77.

__________

78.

Differentiate the function.

__________

79.

Find the derivative of the function.

__________

80.

__________

81.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

__________

82.

Find the limit.

__________

83.

Differentiate the function.

__________

84.

Find the exact value of the expression.

__________

85.

Suppose g is the inverse function of a differentiable function f and

.

If

__________

86.

__________

87.

Use transformations to sketch the graph of the function.

__________

88.

Differentiate the function.

__________

89.

Differentiate the function.

__________

90.

Find the values of

for which

satisfies the equation

__________

91.

Evaluate the integral.

__________

92.

Find the average value of the function on the given interval.

__________

93.

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

__________

94.

Suppose g is the inverse function of a differentiable function f and

.

If

__________

95.

__________

96.

Use logarithmic differentiation to find the derivative of the function.

__________

97.

Find the exponential function

whose graph is given.

__________

98.

Solve the equation for x.

___________

99.

Evaluate the integral.

__________

100.

Differentiate the function.

__________

101.

Find the values of

for which

satisfies the equation

__________

102.

Differentiate the function.

__________

103.

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is

. When will the population reach 50,000?

__________

104.

Find

__________

105.

Find, correct to three decimal places the area of the region above the hyperbola

, below the x axis, and between the lines x = – 4 and x = – 3.

__________

106.

Find an equation of the tangent line to the curve

at the point

.

___________

107.

Evaluate the integral.

__________

108.

Find the limit.

__________

109.

Use l'Hospital's Rule to calculate the exact value of the limit as

__________

110.

Find the inverse function.

__________

111.

Use transformations to sketch the graph of the function.

__________

112.

Suppose g is the inverse function of a differentiable function f and

.
If

__________

113.

Find the solution of the equation correct to four decimal places.

__________

114.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

__________

115.

Find the limit.

__________

116.

Find the volume of the solid obtained by rotating about the y axis the region bounded by the curves.

___________

117.

Evaluate the integral.

__________

118.

__________

119.

If a bacteria population starts with 150 bacteria and doubles every 7 hours, then the number of bacteria after t hours is

When will the population reach 10,000?

__________

120.

Find the derivative of

__________

121.

Find the values of

for which

satisfies the equation

__________

122.

Solve each equation for x.

___________

123.

Find the solution of the equation correct to four decimal places.

__________

124.

Differentiate the function.

__________

125.

__________

126.

Find an equation of the tangent line to the curve at the given point.

___________

127.

Find the absolute minimum value of the function.

__________

128.

If a bacteria population starts with 150 bacteria and doubles every three hours, then the number of bacteria after t hours is

When will the population reach 45,000?

__________

129.

Suppose that the graph of

is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft.

__________

130.

Use logarithmic differentiation to find the derivative of the function.

__________

131.

Find the average value of the function on the given interval.

__________

132.

__________

133.

Find

__________

134.

Find the limit.

__________

135.

Suppose g is the inverse function of a differentiable function f and

.

If

__________

136.

Differentiate the function.

__________

137.

Differentiate the function.

__________

138.

__________

139.

Find

__________

140.

Use logarithmic differentiation to find the derivative of the function.

__________

141.

Evaluate the integral to three decimal places.

__________

142.

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is

When will the population reach 50,000?

__________

143.

Find the limit.

__________

144.

Differentiate the function.

__________

145.

Evaluate the integral.

__________

146.

Evaluate the integral.

__________

147.

Evaluate the integral.

__________

148.

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.