1. Find the first and the second derivatives of the function.
2. Find an equation of the tangent line to the curve.
3. Find
4. Find all points at which the tangent line is horizontal on the graph of the function.
5.
...
1. Find the first and the second derivatives of the function.
2. Find an equation of the tangent line to the curve.
3. Find
4. Find all points at which the tangent line is horizontal on the graph of the function.
5. Calculate .
6. Differentiate the function.
7. The position function of a particle is given by
When does the particle reach a velocity of m/s?
8. If a tank holds 5000 gallons of water, and that water can drain from the tank in 40 minutes, then
Torricelli's Law gives the volume V of water remaining in the tank after t minutes as
.
Find the rate at which water is draining from the tank after minutes.
9. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with
a speed of ft/s. At what rate is his distance from second base decreasing when he is halfway to
first base? Round the result to the nearest hundredth.Stewart - Calculus 8e ET Chapter 3 Form A
© 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.
10. Evaluate
11. Let .
a. Find the derivative of f.
b. Find the point on the graph of f where the tangent line to the curve is horizontal.
c. Sketch the graph of f and the tangent line to the curve at the point found in part (b).
d. What is the rate of change of f at this point?
12. Find the derivative function.
13. A 18-ft ladder leaning against a wall begins to slide. How fast is the angle between the ladder and
the wall changing at the instant of time when the bottom of the ladder is 9 ft from the wall and
sliding away from the wall at the rate of 4 ft/sec? Round the answer to the nearest hundredth.
18 ft
(figure not to scale)
14. Find by implicit differentiation.
15. Find the rate of change of y with respect to x at the given values of x and y.
; x = 4, y = 4Stewart - Calculus 8e ET Chapter 3 Form A
© 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. Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of
intersection of the curves. Show that the curves of the given equations are orthogonal.
y –
74
x = x =
74
cos y
–3 –2 –1 1 2 3 x
3 2 1
–1
–2
–3
y
17. Differentiate the function.
18. s(t) is the position of a body moving along a coordinate line; s(t) is measured in feet and t in
seconds, where . Find the position, velocity, and speed of the body at the indicated time.
; t = 1
19. Two chemicals react to form another chemical. Suppose that the amount of chemical formed in
time t (in hours) is given by
where is measured in pounds.
a. Find the rate at which the chemical is formed when Round to two decimal places.
b. How many pounds of the chemical are formed eventually?
20. A circle’s radius is increasing. Find the rate of change of the area of the circle with respect to the
radius r whenStewart - Calculus 8e ET Chapter 3 Form A
© 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.
Answer Key
1.
2. y = 1
200 (x - 4) + 0.2
3.
4.
5.
6.
7.
8.
9.
10.
11. a.
b. (2, 0)
c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
9 8 7 6 5 4 3 2 1
–1
y
d. 0
12.
13. 0.26 rad/sec
14.
15. 8Stewart - Calculus 8e ET Chapter 3 Form A
© 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. The curves intersect at .
For y – 7
4 x = m =
74
.
For x = 7
4 cos y, m = –
47
csc y; at , m = –
47
.
17.
18. ft, ft/sec, ft/sec
19. a. 0.08 lb/hr, b. 11 lbs
20.Stewart - Calculus 8e ET Chapter 3 Form B
© 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.
1. Find in terms of .
2. If and , find
3. Differentiate.
4. Calculate y’.
5. Differentiate.
6. Differentiate.
7. Find the equation of the tangent line to the given curve at the specified point.
8. Differentiate.
9. Find
10. Calculate .Stewart - Calculus 8e ET Chapter 3 Form B
© 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. Use logarithmic differentiation to find the derivative of the function.
12. 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.
13. Evaluate the integral.
14. Refer to the law of laminar flow. Consider a blood vessel with radius 0.01 cm, length 3 cm,
pressure difference and viscosity 0.028.
Find the velocity of the blood at radius r =
15. The volume of a cube is increasing at a rate of . How fast is the surface area increasing
when the length of an edge is .
16. Find the derivative of the function.
17. Differentiate the function.Stewart - Calculus 8e ET Chapter 3 Form B
© 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.
18. Two chemicals react to form another chemical. Suppose that the amount of chemical formed in
time t (in hours) is given by
where is measured in pounds.
a. Find the rate at which the chemical is formed when Round to two decimal places.
b. How many pounds of the chemical are formed eventually?
19. The volume of a right circular cone of radius r and height h is . Suppose that the radius
and height of the cone are changing with respect to time t.
a. Find a relationship between , , and .
b. At a certain instant of time, the radius and height of the cone are 12 in. and 13 in. and are
increasing at the rate of 0.2 in./sec and 0.5 in./sec, respectively. How fast is the volume of
the cone increasing?
20. Find the derivative of the function.
= sinh –1 7xStewart - Calculus 8e ET Chapter 3 Form B
© 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.
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18. a. 0.08 lb/hr, b. 11 lbs
19. a.
b. 44.8 in.3/secStewart - Calculus 8e ET Chapter 3 Form B
© 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.
20.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
Select the correct answer for each question.
____ 1. Find the derivative of the function.
a.
b.
c.
d.
____ 2. Find the second derivative of the function.
a.
b.
c.
d.
____ 3. Find an equation of the line tangent to the graph of at the point where x = 0.
a.
b.
c.
d.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 4. Find the given derivative by finding the first few derivatives and observing the pattern that occurs.
a.
b.
c.
d.
e. None of these
____ 5. Find the derivative of the function.
a.
b.
c.
d.
____ 6. Find in terms of .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 7. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 8. Find the derivative of the function.
g(t) = tan(cos 2t)
a.
b.
c.
d.
____ 9. Find the tangent line to the ellipse at the point .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 10. Find by implicit differentiation.
a.
b.
c.
d.
____ 11. Find an equation of the tangent line to the curve at the point
(4,1).
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 12. Find an equation of the tangent line to the given curve at the indicated point.
–3 3
4
–4
x
y
a.
b.
c.
d.
____ 13. Differentiate the function.
a.
b.
c.
d.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 14. Use logarithmic differentiation to find the derivative of the function.
a.
b.
c.
d.
e.
____ 15. Use logarithmic differentiation to find the derivative of the function.
a.
b.
c.
d.
e.
____ 16. 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?
a. $214.00, $215.07
b. $229.00, $228.93
c. $214.00, $214.18
d. $229.00, $230.15Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 17. Water flows from a tank of constant cross-sectional area 50 through an orifice of constant
cross-sectional area located at the bottom of the tank. Initially, the height of the water in
the tank was 20 ft, and t sec later it was given by the equation
How fast was the height of the water decreasing when its height was 2 ft?
h
a. ft/sec
b. ft/sec
c. 2
25 ft/sec
d.
ft/sec
____ 18. Find the instantaneous rate of change of the function when
a.
b. 3
c. 9
d.
____ 19. Compute and dy for the given values of x and .
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 3 Form C
© 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.
____ 20. Use the definitions of the hyperbolic functions to find the following limit.
a.
b.
c.
d.
e. None of theseStewart - Calculus 8e ET Chapter 3 Form C
© 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.
Answer Key
1. C
2. D
3. A
4. B
5. A
6. B
7. C
8. A
9. D
10. D
11. D
12. B
13. C
14. E
15. C
16. C
17. D
18. D
19. A
20. DStewart - 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.
Select the correct answer for each question.
____ 1. Use the definition of the derivative to find the derivative of the function.
a.
b.
c.
d.
____ 2. Find the derivative of the function.
a.
b.
c.
d.
____ 3. Differentiate:
a. d.
b. e.
c.
____ 4. Differentiate:
a. d.
b. e.
c.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.
____ 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
© 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.
____ 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
© 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.
____ 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
© 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.
Answer Key
1. A
2. A
3. A
4. B
5. C
6. A
7. B
8. C
9. C
10. A
11. B
12. A
13. E
14. A
15. E
16. C
17. B
18. A
19. A, D
20. A, BStewart - 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.
____ 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
© 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.
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
© 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.
____ 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
© 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.
Answer Key
1. C
2.
3.
4.
5. C
6.
7.
8. C
9.
10.
11.
12. E
13. $214.00, $214.18
14. 1
14 L/sec
15.
16. B
17.
18.
19.
20. 8t cosh (2t2 + 3) sinh (2t2 + 3)Stewart - Calculus 8e ET Chapter 3 Form F
© 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.
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
© 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.
____ 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.Stewart - Calculus 8e ET Chapter 3 Form F
© 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.
____ 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 5Stewart - Calculus 8e ET Chapter 3 Form F
© 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. 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
© 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.
Answer Key
1.
2. C
3. B
4. (0, 0),
5.
6.
7. C
8.
9.
10.
11. A
12.
13. B
14. 7
2 units/sec
15. A
16.
17. dx
18. 74.2099
19. C
20. 16t cosh (4t2 + 8) sinh (4t2 + 8)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.
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
© 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.
____ 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
© 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.
____ 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 3xStewart - 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
© 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.
Answer Key
1.
2.
3. A
4. A
5.
6.
7. C
8.
9.
10. B
11.
12. $60,765.77
13. C
14.
15. A
16.
17.
18. A
19.
20. EStewart - 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.
____ 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 – 1Stewart - 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
© 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. 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
© 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. 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
© 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.
Answer Key
1. A
2.
3.
4. D
5. D
6.
7. A
8.
9.
10. 3
16
11.
12. A
13.
14.
15.
16. D
17.
18.
19.
20. 4
3 dx
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