Stewart – Calculus 8e ET Chapter 2 Form C
____ 20. Use the graph of the function f to find the value(s) of x at which f is not differentiable.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
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y
a. – 3
b. ± 6
c. – 6
d. 3
Stewart – Calculus 8e ET Chapter 2 Form C
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form D
Select the correct answer for each question.
____ 1. Sketch the graph of the function f and evaluate
a.
12345–1–2–3–4–5 x
1
2
3
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5
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–2
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y
0
c.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
2
b.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
0
d.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
2
Stewart – Calculus 8e ET Chapter 2 Form D
____ 2. Use the graph of to guess at the limit , if it exists.
12345–1–2–3–4–5 x
1
2
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y
a. 1
b. 4
c. 3
d. Does not exist
____ 3. Find the vertical asymptotes of the function.
a.
b.
c.
d.
e. none of these
Stewart – Calculus 8e ET Chapter 2 Form D
____ 4. Find the limit.
a.
b.
c.
d.
e. does not exist
____ 5. If for all x, find .
a.
b.
c.
d.
e. does not exist
____ 6. Find the limit , if it exists.
a. –2
b. Does not exist
c. 3
d. 1
Stewart – Calculus 8e ET Chapter 2 Form D
____ 7. Evaluate .
a. 0
b. –2
c. 2
d. Undefined
____ 8. Evaluate the limit, if it exists.
a.
b. 1
c.
d.
e. does not exist
Stewart – Calculus 8e ET Chapter 2 Form D
____ 9. 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
–3
c.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
2
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
–3
Stewart – Calculus 8e ET Chapter 2 Form D
____ 10. For what value of the constant c is the function f continuous on
a.
b.
c.
d.
e.
____ 11. Use the graph to determine where the function is discontinuous.
12345–1–2–3–4–5 x
1
2
3
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y
a. At 1
b. On the interval
c. At 0
d. At
____ 12. Find the limit.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form D
____ 13. Find the horizontal and vertical asymptotes of the graph of the function
.
a. HA , VA
b. HA , VA none
c. HA , VA none
d. HA , VA
____ 14. Let Find the following limits.
a. and
b. and
c. and
d. both
e. both 1
____ 15. The cost (in dollars) of producing x units of a certain commodity is
Find the instantaneous rate of change with respect to x when (This is called the marginal
cost.)
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form D
____ 16. Find an equation of the tangent line to the curve at the point .
a.
b.
c.
d.
e. None of these
____ 17. Find the tangent line to the parabola at the point
a.
b.
c.
d.
e. None of these
____ 18. The cost (in dollars) of producing x units of a certain commodity is
.
Find the average rate of change with respect to x when the production level is changed from
to .
a.
b.
c.
d.
e.
____ 19. At what point is the function not differentiable.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form D
____ 20. The symbol can be used to denote the greatest integer function, which is defined by the
greatest integer n such that Use the graph of the function to find the indicated limit, if it
exists.
a. 0
b. –1
c. –0.3
d. 0.3
Stewart – Calculus 8e ET Chapter 2 Form D
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form E
1. The displacement (in feet) of a certain particle moving in a straight line is given by
where t is measured in seconds. Find the average velocity over the interval
Round your answer to three decimal places.
____ 2. 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 Select the correct answer.
a. ft/s
b. ft/s
c. ft/s
d. ft/s
e. ft/s
3. Find the value of the limit.
4. Find the limit.
____ 5. Find the limit , if it exists. Select the correct answer.
a. 1
b. 3
c. 2
d. Does not exist
Stewart – Calculus 8e ET Chapter 2 Form E
____ 6. Evaluate the limit, if it exists. Select the correct answer.
a.
b.
c. 1
d.
e. does not exist
7. Sketch the graph of the function f and evaluate
____ 8. You are given that , , and . Find the limit
. Select the correct answer.
a. 17
b. –8
c. 0
d. 22
9. Let . Find the following limits.
Stewart – Calculus 8e ET Chapter 2 Form E
____ 10. Find the limit. Select the correct answer.
a.
b.
c.
d.
e.
____ 11. Find the numbers, if any, where the function is discontinuous.
Select the correct answer.
a.
b. 2
c. 1
d. 0
12. Let
Find the value of k that will make f continuous on
13. Find the interval(s) where is continuous.
____ 14. Find the limit.
Select the correct answer.
a.
b. 0
c.
d.
Stewart – Calculus 8e ET Chapter 2 Form E
____ 15. Find the horizontal and vertical asymptotes of the graph of the function
.
Select the correct answer.
a. HA , VA
b. HA , VA none
c. HA , VA none
d. HA , VA
____ 16. Evaluate the limit. Select the correct answer.
a.
b.
c.
d.
e.
17. The cost (in dollars) of producing x units of a certain commodity is
Find the instantaneous rate of change with respect to x when (This is called the marginal
cost.)
____ 18. Find the instantaneous rate of change of the function when
Select the correct answer.
a. –16
b. 20
c. –22
d. 8
Stewart – Calculus 8e ET Chapter 2 Form E
19. The cost (in dollars) of producing x units of a certain commodity is
.
Find the average rate of change with respect to x when the production level is changed from
to .
____ 20. If an equation of the tangent line to the curve at the point where is find
and . Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form E
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form F
1. 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
____ 2. Use the graph of the function to state the value of , if it exists. Select the correct answer.
a.
b.
c. does not exist
d.
e.
3. Sketch the graph of the function f and evaluate
4. Find the limit.