Stewart – Calculus 8e ET Chapter 3 Form F
____ 13. Two sides of a triangle are m and m in length and the angle between them is increasing at a
rate of rad/s. Find the rate at which the area of the triangle is increasing when the angle
between the sides of fixed length is . Select the correct answer.
a.
b.
c.
d.
e.
14. A point moves along the curve . When the point is at , its x-coordinate is
increasing at the rate of 2 units per second. How fast is its y-coordinate changing at that instant of
time?
____ 15. A car leaves an intersection traveling west. Its position 4 sec later is 26 ft from the intersection. At
the same time, another car leaves the same intersection heading north so that its position 4 sec later
is 20 ft from the intersection. If the speeds of the cars at that instant of time are 8 ft/sec and 12
ft/sec, respectively, find the rate at which the distance between the two cars is changing. Round to
the nearest tenth if necessary. Select the correct answer.
a. 13.7 ft/sec
b. 2.7 ft/sec
c. 4.1 ft/sec
d. 32.8 ft/sec
16. Determine the values of x for which the given linear approximation is accurate to within 0.07 at
a = 0.
17. Find the differential of the function at the indicated number.
18. Find the value of the expression accurate to four decimal places.
cosh 5
Stewart – Calculus 8e ET Chapter 3 Form F
____ 19. Find the derivative of the function. Select the correct answer.
= sinh 2x
a. –2 cosh 2x
b. 2 sinh 2x
c. 2 cosh 2x
d. –sinh 2x
20. Find the derivative of the function.
= cosh2 (4t2 + 8)
Stewart – Calculus 8e ET Chapter 3 Form F
Answer Key
Stewart – Calculus 8e ET Chapter 3 Form G
1. Find an equation of the tangent line to the graph of the function at the indicated point.
2. Find the derivative of the function.
____ 3. Find the second derivative of the function. Select the correct answer.
a.
b.
c.
d.
____ 4. If , find
Select the correct answer.
a.
b.
c.
d.
e.
f.
5. Find the derivative of the function.
g(t) = tan(cos 7t)
6. Find the second derivative of the function.
Stewart – Calculus 8e ET Chapter 3 Form G
____ 7. Find an equation of the tangent line to the curve at the point (4,1).
Select the correct answer.
a.
b.
c.
d.
e.
8. Use logarithmic differentiation to find the derivative of the function.
9. Use logarithmic differentiation to find the derivative of the function.
____ 10. Find the instantaneous rate of change of the function when
Select the correct answer.
a. 64
b.
c. 8
d.
11. Let C (t) be the total value of US currency (coins and banknotes) in circulation at time. The table
gives values of this function from 1980 to 2000, as of September 30, in billions of dollars.
Estimate the value of C (1990) .
t 1980 1985 1990 1995 2000
C(t) 129.9 568.6
Answers are in billions of dollars per year. Round your answer to two decimal places.
12. The parents of a child wish to establish a trust fund for the child’s college education. If they need
an estimated $80,000 5 years from now and they are able to invest the money at 5.5% compounded
continuously in the interim, how much should they set aside in trust now?
Stewart – Calculus 8e ET Chapter 3 Form G
____ 13. The half-life of cesium-137 is 30 years. Suppose we have a -mg sample. Find the mass that
remains after years. Select the correct answer.
a.
b.
c.
d.
e.
14. Strontium- has a half-life of days. A sample has a mass of mg initially. Find a formula
for the mass remaining after days.
____ 15. Use differentials to estimate the amount of paint needed to apply a coat of paint cm thick
to a hemispherical dome with diameter m. Select the correct answer.
a.
b.
c.
d.
e.
16. Use the linear approximation of the function at to approximate the number
.
17. Determine the values of x for which the given linear approximation is accurate to within 0.07 at
a = 0.
____ 18. Find the derivative of the function. Select the correct answer.
= sinh 3x
a. 3 cosh 3x
b. –3 cosh 3x
c. 3 sinh 3x
d. –sinh 3x
Stewart – Calculus 8e ET Chapter 3 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19. 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.
____ 20. At what point of the curve does the tangent line have slope ?
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 3 Form G
Answer Key
Stewart – Calculus 8e ET Chapter 3 Form H
____ 1. Find the derivative of the function. Select the correct answer.
a.
b.
c.
d.
2. Find the derivative of the function.
3. Find the derivative of the function.
____ 4. Find the derivative of the function. Select the correct answer.
= 6 cos x – x + 2
a. 6 cos x – 1
b. –6 cos x – 1
c. 6 sin x – 1
d. –6 sin x – 1
Stewart – Calculus 8e ET Chapter 3 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 5. Find the derivative of the function. Select the correct answer.
a.
b.
c.
d.
6. Calculate
.
____ 7. Find the derivative of the function. Select the correct answer.
g(t) = tan(cos 4t)
a.
b.
c.
d.
8. Find
in terms of x and y.
9. Find the derivative of the function.
10. If , find .
Stewart – Calculus 8e ET Chapter 3 Form H
11. Use implicit differentiation to find dy/dx.
____ 12. The quantity Q of charge in coulombs C that has passed through a point in a wire up to time t
(measured in seconds) is given by
.
Find the current when . Select the correct answer.
a.
b.
c.
d.
e.
13. The mass of part of a wire is kilograms, where x is measured in meters from one end
of the wire. Find the linear density of the wire when x m .
14. If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its
image will be at a distance u from the lens, where f, v, and u are related by the lens equation
.
Find the rate of change of v with respect to u.
15. If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the
interest is compounded annually.
Stewart – Calculus 8e ET Chapter 3 Form H
____ 16. Gravel is being dumped from a conveyor belt at a rate of ft/min and its coarseness is such that
it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is
the height of the pile increasing when the pile is ft high? Round the result to the nearest
hundredth. Select the correct answer.
a.
b.
c.
d.
e.
17. Use the linear approximation of the function at to approximate the number
.
18. A turkey is removed from the oven when its temperature reaches and is placed on a table in
a room where the temperature is . After 10 minutes the temperature of the turkey is
and after 20 minutes it is . Use a linear approximation to predict the temperature of the
turkey after minutes.
19. Compute
and dy for the given values of x and .
20. Find the differential of the function at the indicated number.
Stewart – Calculus 8e ET Chapter 3 Form H
Answer Key