Stewart – Calculus 8e ET Chapter 3 Form D
____ 5. Find
a. d.
b. e.
c.
____ 6. Find
in terms of .
a.
b.
c.
d.
e.
____ 7. If , find
a.
b.
c.
d.
e.
f.
Stewart – Calculus 8e ET Chapter 3 Form D
© 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.
____ 8. Calculate
.
a.
b.
c.
d.
e.
____ 9. Suppose that and , , , and .
Find .
a. 24
b. 17
c.
d. 140
e. 20
____ 10. If , find .
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 3 Form D
© 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.
____ 11. Find the derivative of the function.
g(t) = tan(cos 9t)
a.
b.
c.
d.
____ 12. Use implicit differentiation to find an equation of the tangent line to the curve at the indicated
point.
y = sin xy2;
a. y = 1
b. y = x
c. x =
d. y = 2x + 1
____ 13. The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the
acceleration after seconds.
a.
b.
c.
d.
e.
____ 14. A curve passes through the point and has the property that the slope of the curve at every
point is twice the -coordinate of . What is the equation of the curve?
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 3 Form D
____ 15. A plane flying horizontally at an altitude of 1 mi and a speed of mi/h passes directly over a
radar station. Find the rate at which the distance from the plane to the station is increasing when it
is 2 mi away from the station.
a.
b.
c.
d.
e.
____ 16. An equation relating the variables x and y, the values of x and y, and the value of at a
particular instant of time are given. Find the value of .
a.
2
b.
2
c.
4
d.
4
____ 17. Determine the values of x for which the given linear approximation is accurate to within 0.07 at
a = 0.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 3 Form D
____ 18. Find the given integral.
a. sinh (2x + 3) + C
b. sinh (2x + 3)+ C
c. –sinh (2x + 3)+ C
d. 2sinh (2x + 3) + C
____ 19. If , find and .
a.
b.
c.
d.
e.
____ 20. Find equations of the tangent lines to the curve that are parallel to the line .
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 3 Form D
Answer Key
Stewart – Calculus 8e ET Chapter 3 Form E
____ 1. Find an equation of the tangent line to the graph of the function at the indicated point.
Select the correct answer.
a.
b.
c.
d.
2. Find the derivative of the function.
3. Find the second derivative of the function.
4. If , find
____ 5. Find
in terms of . Select the correct answer.
a.
b.
c.
d.
e.
6. Find the derivative of the function.
g(t) = tan(cos 2t)
Stewart – Calculus 8e ET Chapter 3 Form E
7. Find the second derivative of the function.
____ 8. If u is a differentiable function of x and f (x) = |u| then .
Use this to find the derivative of the following function. Select the correct answer.
f (x) = |x2 – 4|
a.
b.
c.
d.
9. Calculate y’.
10. Use logarithmic differentiation to find the derivative of the function.
11. Evaluate the integral.
Stewart – Calculus 8e ET Chapter 3 Form E
____ 12. Find the average rate of change of the area of a circle with respect to its radius r as r changes from
to . Select the correct answer.
a.
b.
c.
d.
e.
13. Suppose the daily total cost (in dollars) of manufacturing x televisions is
What is the marginal cost when x = 200? What is the actual cost incurred in manufacturing the
201st television?
14. In an adiabatic process (one in which no heat transfer takes place), the pressure P and volume V of
an ideal gas such as oxygen satisfy the equation
,
where C is a constant. Suppose that at a certain instant of time, the volume of the gas is 2L, the
pressure is 100 kPa, and the pressure is decreasing at the rate of 5 kPa/sec. Find the rate at which
the volume is changing.
15. 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.
Stewart – Calculus 8e ET Chapter 3 Form E
© 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.
____ 16. 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) . Select the correct answer.
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.
a.
b.
c.
d.
e.
17. The half-life of cesium-137 is 30 years. Suppose we have a -mg sample. Find the mass that
remains after years.
18. Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass
remaining after 42 days.
19. 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.
20. Find the derivative of the function.
= cosh2 (2t2 + 3)
Stewart – Calculus 8e ET Chapter 3 Form E
Answer Key
Stewart – Calculus 8e ET Chapter 3 Form F
1. Find the second derivative of the function.
____ 2. Find an equation of the line tangent to the graph of at the point where x = 0.
Select the correct answer.
a.
b.
c.
d.
____ 3. Find the derivative of the function. Select the correct answer.
= 7 sin x – 7x + 2
a. –7 sin x – 7
b. 7 cos x – 7
c. 7 sin x – 7
d. –7 cos x – 7
4. Find the point(s) on the graph of f where the tangent line is horizontal.
5. Find the derivative of the function.
6. If u is a differentiable function of x and f (x) = |u| then .
Use this to find the derivative of the following function.
f (x) = |x2 – 49|
Stewart – Calculus 8e ET Chapter 3 Form F
____ 7. Use implicit differentiation to find an equation of the tangent line to the curve at the indicated
point. Select the correct answer.
y = sin xy7;
a. y = x
b. x =
c. y = 1
d. y = 7x + 1
8. Find
in terms of x and y.
9. Differentiate the function.
10. Differentiate the function.
____ 11. The mass of the part of a metal rod that lies between its left end and a point x meters to the right is
.
Find the linear density when x is m. Select the correct answer.
a.
b.
c.
d.
e.
12. Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass
remaining after 48 days.