Stewart – Calculus 8e ET Chapter 2 Form F
____ 5. If for all x, find . Select the correct answer.
a.
b.
c.
d.
e. does not exist
6. Find the limit , if it exists.
____ 7. Evaluate the limit, if it exists. Select the correct answer.
a. 1
b.
c.
d.
e. does not exist
Stewart – Calculus 8e ET Chapter 2 Form F
8. 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
____ 9. Use the graph of to guess at the limit , if it exists.
Select the correct answer.
0.5 1–0.5–1 x
0.25
0.5
0.75
1
1.25
1.5
–0.25
–0.5
y
a. Does not exist
b. 0.8
c. 1.3
d. 0.2
Stewart – Calculus 8e ET Chapter 2 Form F
10. Estimate the value of the limit by graphing the function . State your answer correct to two
decimal places.
11. Find the limit.
____ 12. Which of the given functions is discontinuous? Select the correct answer.
a.
b.
13. For what value of the constant c is the function f continuous on
Stewart – Calculus 8e ET Chapter 2 Form F
____ 14. Find the limit. Select the correct answer.
a.
b.
c.
d.
e.
15. Find the limit.
16. Find the horizontal and vertical asymptotes of the graph of the function
.
____ 17. Use the definition of the derivative to find
Select the correct answer.
a.
b.
c.
d.
e. does not exist
18. Find an equation of the tangent line to the curve at the point .
19. The slope of the tangent line to the graph of the exponential function at the point is
Estimate the slope to three decimal places.
Stewart – Calculus 8e ET Chapter 2 Form F
____ 20. Find the tangent line to the parabola at the point Select the correct answer.
a.
b.
c.
d.
e. None of these
Stewart – Calculus 8e ET Chapter 2 Form F
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form G
1. Estimate the value of the following limit by graphing the function .
Round your answer correct to two decimal places.
2. Use the graph of the function to state the value of if it exists.
____ 3. Use the graph of the function to state the value of , if it exists. Select the correct answer.
a.
b. does not exist
c.
d.
e.
____ 4. Find the value of . Select the correct answer.
.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form G
5. Find the limit by evaluating the derivative of a suitable function at an appropriate value of x.
(Hint: Use the definition of the derivative.)
6. Is there a number a such that exists? If so, find the value of a and the value
of the limit.
7. Sketch the graph of the function f and evaluate
8. Sketch the graph of the function f and evaluate
Stewart – Calculus 8e ET Chapter 2 Form G
____ 9. Use the graph of to guess at the limit , if it exists.
Select the correct answer.
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
10. If f and g are continuous functions with
11. Let
and be polynomials.
Find if the degree of is and the degree of is .
12. A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and
before deploying her parachute is given by
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
Stewart – Calculus 8e ET Chapter 2 Form G
____ 13. Evaluate the limit. Select the correct answer.
a.
b.
c.
d.
e.
14. Let Find the following limits.
15. Use the definition of the derivative to find
____ 16. Find an equation of the tangent line to the parabola at the point .
Select the correct answer.
a.
b.
c.
d.
e.
17. If an equation of the tangent line to the curve at the point where is find
and .
____ 18. At what point is the function not differentiable. Select the correct answer.
a.
b.
c.
d.
e.
19. If use the definition of derivative to find
_
Stewart – Calculus 8e ET Chapter 2 Form G
___ 20. Match the graph of the function with the graph of its derivative.
0
x
y
a.
0
x
y
c.
0
x
y
b.
0
x
y
d.
0
x
y
Stewart – Calculus 8e ET Chapter 2 Form G
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form G
Stewart – Calculus 8e ET Chapter 2 Form H
1. If a rock is thrown upward on the planet Mars with a velocity of , its height in meters t
seconds later is given by
.
Find the average velocity over the time interval .
2. Use the graph of the function to state the value of if it exists.
3. Sketch the graph of the function f and evaluate
____ 4. Find the limit . Select the correct answer.
a. 7
b. 3
c. 5
d. –7
____ 5. Find the limit by evaluating the derivative of a suitable function at an appropriate value of x.
(Hint: Use the definition of the derivative.) Select the correct answer.
a. 25
b. 75
c.
d.
Stewart – Calculus 8e ET Chapter 2 Form H
____ 6. If , then if exists, find the value where it exists. Select the correct answer.
a. 1
b.
c.
d.
e.
7. Sketch the graph of the function f and evaluate
8. Sketch the graph of the function f and evaluate
____ 9. 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. Select the correct answer.
a. 0
b. 1
c. –0.7
d. 0.7
____ 10. You are given that , , and . Find the limit
. Select the correct answer.
a. 17
b. –8
c. 0
d. 22
Stewart – Calculus 8e ET Chapter 2 Form H
11. You are given and a tolerance Find a number such that
whenever
____ 12. How would you define in order to make f continuous at ? Select the correct answer.
a.
b.
c.
d.
e. None of these
____ 13. Find the numbers, if any, where the function is discontinuous.
Select the correct answer.
a.
b. 2
c. 1
d. 0
14. Define the function at 0 so as to make it continuous at 0.
____ 15. Find the limit. Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 2 Form H
16. Find the horizontal and vertical asymptotes of the graph of the function
.
17. Use the definition of the derivative to find
____ 18. If the tangent line to passes through the point
Select the correct answer.
a.
b.
c.
d.
e.
19. Find the slope of the tangent line to the curve at the point .
20. Find the instantaneous rate of change of the function when
Stewart – Calculus 8e ET Chapter 2 Form H
Answer Key
Stewart – Calculus 8e ET Chapter 2 Form H