## Single Variable Calculus 8th Edition By James Stewart – Test Bank

Stewart – Calculus 8e Chapter 1 Form A

1. Find the domain of the function.

2. Determine whether f is even, odd, or neither.

3. The graphs of and are given. a) For what values of is ? b) Find the values of and .

4. It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in of the caves by the equation

(a) The cave called mission impossible near puebla, mexico, has suface area of . How many species of bats would expect to find in that cave?

(b) If you discover that species of bats live in cave estimate the area of the cave.

Stewart – Calculus 8e Chapter 1 Form A

5. Express the function in the form of .

6. The position of a car is given by the values in the following table.

Estimate the instantaneous velocity when by averaging the velocities for the periods .

7. Consider the following function.

Determine the values of a for which exists.

8. Find the limit.

9. Evaluate the limit.

10. Find the limit.

Stewart – Calculus 8e Chapter 1 Form A

11. Evaluate the limit.

12. Evaluate the limit.

13. Evaluate the limit.

14. Find a number such that if , then , where .

15. Find the point at which the given function is discontinuous.

16. Write an equation that expresses the fact that a function f is continuous at the number .

17. Find a function g that agrees with f for and is continuous on .

18. Let and . Find .

19. Find the limit .

20. Find the numbers, if any, where the function is discontinuous.

Stewart – Calculus 8e Chapter 1 Form A Answer Key

1.

2. even

3. a) –2, 10 b) ,

4. a) species b)

5.

6. ft/s

7.

8.

9.

10. 0

11.

12.

13.

14.

15.

Stewart – Calculus 8e Chapter 1 Form A 16.

17.

18. –6

19.

20.

Stewart – Calculus 8e Chapter 1 Form B

1. Find the domain of the function.

2. A spherical balloon with radius inches has volume .

Find a function that represents the amount of air required to inflate the balloon from a radius of inches to a radius of inches.

3. It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in of the caves by the equation

(a) The cave called mission impossible near puebla, mexico, has suface area of . How many species of bats would expect to find in that cave?

(b) If you discover that species of bats live in cave estimate the area of the cave.

4. A spherical balloon with radius inches has volume

. Find a function that represents the amount of air required to inflate the balloon from a radius of inches to a radius of inches.

5. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s. Express the radius r of this circle as a function of the time t (in seconds) and find if A is the area of this circle as a function of the radius.

6. The position of a car is given by the values in the following table.

Estimate the instantaneous velocity when by averaging the velocities for the periods .

Stewart – Calculus 8e Chapter 1 Form B 7. Evaluate the function

at the given numbers (correct to six decimal places). Use the results to guess the value of the limit

8. By graphing the function

and zooming in toward the point where the graph crosses the y-axis, estimate the value of

Stewart – Calculus 8e Chapter 1 Form B 9. Consider the following function.

Determine the values of a for which exists.

10. How close to 2 do we have to take x so that is within a distance of 0.01 from 13?

11. Find the limit.

12. Evaluate the limit.

13. Find the limit.

14. Evaluate the limit.

15. Find the limit if .

16. Use a graph to find a number such that whenever .

Stewart – Calculus 8e Chapter 1 Form B

17. If f and g are continuous functions with

18. The following figure shows a portion of the graph of a function f defined on the interval . Sketch the complete graph of f if it is known f is odd.

1–1 x

1

–1

y

19. Let and . Find .

20. Find the limit , if it exists.

Stewart – Calculus 8e Chapter 1 Form B Answer Key

1.

2.

3. a) species b)

4. 12

5.

6. ft/s

7.

8.

9.

10.

11.

12. 10 7

13. 0

14.

15.

16.

17.

Stewart – Calculus 8e Chapter 1 Form B 18.

1–1 x

1

–1

y

19. –6

20.

Stewart – Calculus 8e Chapter 1 Form C

Select the correct answer for each question.

____ 1. If , evaluate the difference quotient .

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

____ 2. Find the domain of the function

a. b.

c.

d.

Stewart – Calculus 8e Chapter 1 Form C

____ 3. The graph of the function is given. State the value of .

a. b. c. d. e.

____ 4. Scientists have discovered that a linear relationship exists between the amount of flobberworm mucus secretions and the air temperature. When the temperature is 65°F, the flobberworms each secrete 16 grams of mucus a day; when the temperature is 95°F, they each secrete 22 grams of mucus a day. Find a function M(t) that gives the amount of mucus secreted on a given day, where t is the temperature of that day in degrees Fahrenheit.

a. b. c. d.

Stewart – Calculus 8e Chapter 1 Form C

____ 5. Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

a.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

c.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

b.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

d.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Stewart – Calculus 8e Chapter 1 Form C

____ 6. Sketch the graph of over one period.

a.

12345678–1–2 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

c.

12345678–1–2 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

b.

12345678–1–2 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

d.

12345678–1–2 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Stewart – Calculus 8e Chapter 1 Form C

____ 7. The graph of the function has been stretched horizontally by a factor of 2. Find the function for the transformed graph.

a.

b.

c.

d.

____ 8. A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient’s heart rate after 42 minutes using the secant line between the points with .

a. b. c. d. e. f.

____ 9. If a ball is thrown into the air with a velocity of , its height (in feet) after t seconds is given by

.

Find the velocity when

a. ft/s b. ft/s c. ft/s d. ft/s

Stewart – Calculus 8e Chapter 1 Form C

____ 10. The position of a car is given by the values in the following table.

(seconds) 0 1 2 3 4 (meters) 0 21.9 25.8 69.2 92.2

Find the average velocity for the time period beginning when and lasting 2 seconds.

a. ft/s b. ft/s c. 33.5 ft/s d. ft/s e. 33.2 ft/s

____ 11. Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function Calculate the (instantaneous) velocity of the car when

a. 223 ft/sec b. 16 ft/sec c. 560 ft/sec d. 4130 ft/sec

Stewart – Calculus 8e Chapter 1 Form C

____ 12. Sketch the graph of the function f and evaluate

a.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Does not exist

c.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Does not exist

b.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

2

d.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

5

Stewart – Calculus 8e Chapter 1 Form C

____ 13. Evaluate the limit.

a. b. c. d. e.

____ 14. If find

a. b. c. 0 d. e.

____ 15. Find the limit.

a. b. c. d. e.

Stewart – Calculus 8e Chapter 1 Form C

____ 16. Use the graph of to guess at the limit , if it exists.

12345–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

a. –2 b. –1 c. Does not exist d. –3

____ 17. Let . Find the following limits.

a. b. c. d. e.

Stewart – Calculus 8e Chapter 1 Form C

____ 18. Which of the given functions is discontinuous?

a.

b.

____ 19. Find the numbers, if any, where the function is discontinuous.

a. b. 2 c. 1 d. 0

____ 20. Find the interval(s) where is continuous.

a. b. c. d.

Stewart – Calculus 8e Chapter 1 Form C Answer Key

1. E

2. A

3. C

4. D

5. C

6. C

7. C

8. F

9. B

10. E

11. A

12. D

13. D

14. B

15. A

16. C

17. D

18. A

19. C

20. C

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