1. Find the limit.
2. Evaluate the limit.
3. Find the limit.
4. How close to do we have to take x so that
5. How close to 2 do we have to take x so that is within a distance of 0.01 from 13?
6. If f and g are contin
...
1. Find the limit.
2. Evaluate the limit.
3. Find the limit.
4. How close to do we have to take x so that
5. How close to 2 do we have to take x so that is within a distance of 0.01 from 13?
6. If f and g are continuous functions with
7. Find the limit.
8. Find the limit.
9. Find an equation of the tangent line to the curve.Stewart - Calculus 8e ET Chapter 2 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. Find the limit if
11. Use the graph of the function to find each limit.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
, ,
12. Complete the table by computing at the given values of x, accurate to five decimal places.
Use the results to guess at the indicated limit, if it exists, to three decimal places.
x 3.9 3.99 3.999 4.001 4.01 4.1
13. Use the precise definition of a limit to prove that
14. Find the limit .
15. Find the numbers, if any, where the function is discontinuous.Stewart - Calculus 8e ET Chapter 2 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. Find the interval(s) where is continuous.
17. You are given the graph of f. Find the horizontal and vertical asymptotes of the graph of f.
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x
7 6 5 4 3 2 1
–1
–2
–3
–4
–5
–6
–7
y
18. The graph shows the percentage of households in a certain city watching television during a 24-hr period on
a weekday ( corresponds to 6 a.m.). By computing the slope of the respective tangent line, estimate the
rate of change of the percentage of households watching television at a-12 p.m.
Note that
3
dy
2 4 6 8 10 12 14 16 18 20 t (hr)
0.075
0.15
0.225
y (%)
19. Find the derivative of the function and evaluate at the given value of x.Stewart - Calculus 8e ET Chapter 2 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.
20. Let .
a. Sketch the graph of f.
b. For what values of x is f differentiable?
c. Find a formula for .Stewart - Calculus 8e ET Chapter 2 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. 0
3. 0
4.
5.
6.
7.
8.
9.
10.
11. , ,
12.
x 3.9 3.99 3.999 4.001 4.01 4.1
0.1252 0.12502 0.125 0.125 0.12498 0.12481
0.125
13. The function is and
Let be given. Choose to be any real number greater than 0.
We see that for any x such that (actually for any x whatsoever), we have
This proves the assertion.
14.
15.
16.
17. HA , VA
18. Falling at
19. 225
2Stewart - Calculus 8e ET Chapter 2 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.
20. a.
–4 –2 2 4 x
5
10
–5
–10
y
b.
c.Stewart - Calculus 8e ET Chapter 2 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. 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
.
2. Find the limit.
3. Evaluate the limit.
4. Evaluate the limit.
5. Find the limit.
6. Consider the following function.
Determine the values of a for which exists.Stewart - Calculus 8e ET Chapter 2 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.
7. How close to do we have to take x so that
8. Use a graph to find a number such that whenever .
Round your answer to the nearest thousandth.
9. Use the definition of the limit to find values of that corresponds to .
Round your answer to the nearest thousandth.
10. Use a graph to find a number such that whenever .
11. How close to 2 do we have to take x so that is within a distance of 0.01 from 13?
12. Use continuity to evaluate the limit.
13. For the function f whose graph is shown, state the following.Stewart - Calculus 8e ET Chapter 2 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.
14. If a cylindrical tank holds gallons of water, which can be drained from the bottom of the
tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after t
minutes as
Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V
with respect to t) as a function of t.
15. Find an equation of the tangent line to the curve at the point (1, 1).
16. Use the graph of the function to find each limit.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
, ,
17. Use the precise definition of a limit to prove that
18. Find the limit.Stewart - Calculus 8e ET Chapter 2 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.
19. Sketch the graph of the derivative of the function f whose graph is given.
–5 –4 –3 –2 –1 1 2 3 4 5 x
6 5 4 3 2 1
y
20. Let .
a. Sketch the graph of f.
b. For what values of x is f differentiable?
c. Find a formula for .Stewart - Calculus 8e ET Chapter 2 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. ft/s
2.
3. 10
7
4.
5. 0
6.
7.
8.
9.
10.
11.
12. 21
5
13.
14.
15.
16. , , Does not exist
17. The function is and
Let be given. Choose to be any real number greater than 0.
We see that for any x such that (actually for any x whatsoever), we have
This proves the assertion.
18. 0Stewart - Calculus 8e ET Chapter 2 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.
19.
–5 –4 –3 –2 –1 1 2 3 4 5 x
4 3 2 1
–1
–2
–3
–4
y
20. a.
–4 –2 2 4 x
5
10
–5
–10
y
b.
c.Stewart - Calculus 8e ET Chapter 2 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. 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
____ 2. 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 .
a. m/s
b. m/s
c. m/s
d. m/s
e. m/s
____ 3. The point lies on the curve . If is the point Q , use your calculator to
find the slope of the secant line PQ (correct to six decimal places) for the value
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 2 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. Use the graph of the function to state the value of if it exists.
a.
b.
c. does not exist
d. 1
e.Stewart - Calculus 8e ET Chapter 2 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.
____ 5. Sketch the graph of the function f and evaluate
a.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
1
c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
3
b.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
3
d.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
1Stewart - Calculus 8e ET Chapter 2 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.
____ 6. Evaluate the limit.
a.
b.
c.
d.
e.
____ 7. Find the limit , if it exists.
a. 1
b. 3
c. 2
d. Does not exist
____ 8. Find the limit by evaluating the derivative of a suitable function at an appropriate value of x.
(Hint: Use the definition of the derivative.)
a. 25
b. 75
c.
d.
____ 9. You are given that , , and . Find the limit
.
a. 17
b. –8
c. 0
d. 22Stewart - Calculus 8e ET Chapter 2 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 the limit.
a. 0
b.
c.
d.
e. does not exist
____ 11. A machinist is required to manufacture a circular metal disk with area 1000 . If the machinist is
allowed an error tolerance of in the area of the disk, how close to the ideal radius must the
machinist control the radius?
Round your answer to the nearest hundred thousandth.
a.
b.
c.
d.
e.
____ 12. If f and g are continuous functions with
a.
b.
c.
d.
e.Stewart - Calculus 8e ET Chapter 2 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.
____ 13. Use the graph to determine where the function is discontinuous.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a. At 0
b. On the interval
c. At
d. At 1
____ 14. Find the numbers, if any, where the function is discontinuous.
a.
b. 2
c. 1
d. 0
____ 15. Let
Find the value of k that will make f continuous on
a. 5
b. 46
c. –4
d. 3Stewart - Calculus 8e ET Chapter 2 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.
____ 16. Find the limit.
a.
b. 0
c.
d.
____ 17. 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 , VAStewart - Calculus 8e ET Chapter 2 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.
____ 18. Find the vertical asymptotes of the function.
a.
b.
c.
d.
e. None of these
____ 19. If use the definition of derivative to find
a.
b.
c.
d.
e. None of theseStewart - Calculus 8e ET Chapter 2 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 graph of the function f to find the value(s) of x at which f is not differentiable.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
a. – 3
b. ± 6
c. – 6
d. 3Stewart - Calculus 8e ET Chapter 2 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. A
2. C
3. E
4. C
5. D
6. D
7. B
8. A
9. B
10. C
11. D
12. E
13. C
14. C
15. D
16. D
17. B
18. E
19. D
20. DStewart - Calculus 8e ET Chapter 2 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. Sketch the graph of the function f and evaluate
a.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
0
c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
2
b.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
0
d.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
2Stewart - Calculus 8e ET Chapter 2 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.
____ 2. Use the graph of to guess at the limit , if it exists.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
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 theseStewart - Calculus 8e ET Chapter 2 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.
____ 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. 1Stewart - Calculus 8e ET Chapter 2 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.
____ 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 existStewart - Calculus 8e ET Chapter 2 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.
____ 9. Sketch the graph of the function f and evaluate
a.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
–3
c.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
2
b.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
2
d.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
–3Stewart - Calculus 8e ET Chapter 2 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.
____ 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.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
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
© 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. 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
© 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. 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
© 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. 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. 0.3Stewart - Calculus 8e ET Chapter 2 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. C
2. B
3. E
4. A
5. A
6. D
7. C
8. C
9. C
10. C
11. D
12. E
13. B
14. A
15. E
16. E
17. D
18. C
19. E
20. BStewart - Calculus 8e ET Chapter 2 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. 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 existStewart - Calculus 8e ET Chapter 2 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.
____ 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
© 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 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
© 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. 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. 8Stewart - Calculus 8e ET Chapter 2 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.
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
© 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. B
3.
4.
5. B
6. D
7.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
3
8. B
9.
10. C
11. C
12. 3
13.
14. D
15. B
16. C
17.
18. B
19.
20. DStewart - Calculus 8e ET Chapter 2 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. 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.Stewart - Calculus 8e ET Chapter 2 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.
____ 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 existStewart - Calculus 8e ET Chapter 2 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.
8. Use the graph of to guess at the limit , if it exists.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
____ 9. Use the graph of to guess at the limit , if it exists.
Select the correct answer.
–1 –0.5 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. 0.2Stewart - Calculus 8e ET Chapter 2 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.
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 onStewart - Calculus 8e ET Chapter 2 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.
____ 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
© 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. Find the tangent line to the parabola at the point Select the correct answer.
a.
b.
c.
d.
e. None of theseStewart - Calculus 8e ET Chapter 2 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. ft/s
2. C
3.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
2
4.
5. A
6.
7. C
8. Does not exist
9. B
10.
11.
12. B
13.
14. B
15.
16. HA , VA none
17. A
18. None of these
19.
20. AStewart - Calculus 8e ET Chapter 2 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. 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
© 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 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 evaluateStewart - Calculus 8e ET Chapter 2 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.
____ 9. Use the graph of to guess at the limit , if it exists.
Select the correct answer.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–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: EvaluateStewart - Calculus 8e ET Chapter 2 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. 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
© 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. 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
yStewart - Calculus 8e ET Chapter 2 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. does not exist
3. B
4. A
5. 25
6. , limit equals
7.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
–1
8.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
3
9. C
10.
11.
12. m/sec
13. C
14. and
15.Stewart - Calculus 8e ET Chapter 2 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.
16. C
17.
18. B
19.
20. BStewart - Calculus 8e ET Chapter 2 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. 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
© 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.
____ 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. 22Stewart - Calculus 8e ET Chapter 2 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. 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
© 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. 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 whenStewart - Calculus 8e ET Chapter 2 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. m/s
2. does not exist
3.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
5
4. D
5. A
6. C
7.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
–1Stewart - Calculus 8e ET Chapter 2 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.
8.
–5 –4 –3 –2 –1 1 2 3 4 5 x
5 4 3 2 1
–1
–2
–3
–4
–5
y
3
9. A
10. B
11. 0.0025
12. B
13. C
14.
15. C
16. HA , VA none
17.
18. C
19.
20. 20
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