8.5 Partial Functions
514
8.5 Partial Functions
Answer Section
515 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.6 Integration of Tables and Other Integration Techniques
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use integration tables to find .
a.
b.
c.
d.
e.
____ 2. Use integration tables to find .
a.
b.
c.
d.
e.
8.6 Integration of Tables and Other Integration Techniques
516
____
3.
Use integration tables to find
.
a.
b.
c.
d.
e.
____
4.
Use integration tables to find
.
a.
b.
c.
d.
e.
____
5.
Use integration tables to find the integral
.
a.
b.
c.
d.
e.
517 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 6. Use integration tables to find .
a.
b.
c.
d.
e.
____ 7. Use integration tables to evaluate the integral .
a.
b.
c.
d.
e.
____ 8. Use integration tables to evaluate the integral .
a.
b.
c.
d.
e.
8.6 Integration of Tables and Other Integration Techniques
518
____ 9. Use integration tables to evaluate the integral .
a.
b.
c.
d.
e.
____ 10. Evaluate the integral .
a.
b.
c.
d.
e.
____ 11. A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet
where the variable force required is pounds. Find the work done in
pushing the block the full feet through the machine. Round your answer to three decimal places.
a.
b.
c.
d.
e.
519 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 12.
A population is growing according to the logistic model
, where t
is the time in days. Find the average population over the interval
. Round your answer to one
decimal place.
a.
b.
c.
d.
e.
____ 13. Use a table of integrals to find the integral.
a.
b.
c.
d.
e.
8.6 Integration of Tables and Other Integration Techniques
520
____
14.
Use a table of integrals with forms involving the trigonometric functions to find the
integral.
a.
b.
c.
d.
e.
____
15.
Find the integral using integration by parts.
a.
b.
c.
d.
e.
521 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.6 Integration of Tables and Other Integration Techniques
Answer Section
8.7: Indeterminate Forms and L’Hôpital’s Rule
522
8.7 Indeterminate Forms and L’Hôpital’s Rule
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the limit first by using techniques from Chapter 1 then
by using L’Hopital’s Rule.
a.
b.
c.
0
does not exist
____ 2. Evaluate the limit first by using techniques from Chapter 1
then by using L’Hopital’s Rule.
a.
0
does not exist
____ 3. Evaluate the limit first by using techniques from Chapter 3 then
by using L’Hopital’s Rule.
a.
b.
c.
does not exist
523 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 4. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
1
0
does not exist
____ 5. Evaluate the limit using L’Hopital’s Rule if necessary.
0
____
6.
Evaluate the limit
using L’Hopital’s Rule if necessary.
a.
b.
0
c.
d.
e.
does not exist
____
7.
Evaluate the
using L’Hôpital’s Rule if necessary.
a.
b.
c.
d.
0
e.
8.7: Indeterminate Forms and L’Hôpital’s Rule
524
____
8.
Evaluate the
using L’Hôpital’s Rule if necessary.
a.
b.
c.
d.
e.
0
____
9.
Evaluate the limit
using L’Hopital’s Rule if necessary.
a.
0
b.
c.
1
does not exist
____ 10. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e. 0
____ 11. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
0
525 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 12. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e.
____ 13. Evaluate the limit using L’Hopital’s Rule if necessary.
0
does not exist
____ 14. Evaluate the limit using L’Hopital’s Rule if necessary.
1
____ 15. Evaluate the limit using L’Hopital’s Rule if necessary.
1
0
8.7: Indeterminate Forms and L’Hôpital’s Rule
526
____
16.
Evaluate the limit
using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e.
does not exist
____
17.
Apply the Extended Mean Value Theorem to the functions
and
on the interval
, and find all values c in the interval
such that
.
a.
b.
c.
d.
e.
8
3
527 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.7 Indeterminate Forms and L’Hôpital’s Rule
Answer Section
8.8 Improper Integrals
528
8.8 Improper Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____ 2. Determine whether the improper integral diverges or converges. Evaluate
the integral if it converges.
a.
b.
c.
diverges
____ 3. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
529 Chapter 8: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
____ 4. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
18
9
3
diverges
____
5.
Determine whether the improper integral
diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____
6.
Determine whether the improper integral
diverges or converges.
Evaluate the integral if it converges.
a.
b.
____
7.
Determine whether the improper integral
diverges or converges.
a.
b.
8.8 Improper Integrals
530
____ 8. Determine whether the improper integral diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e. diverges
____
9.
Determine whether the improper integral
diverges or converges.
a.
b.
____
10.
Determine whether the improper integral
diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
d.
e.
diverges
____
11.
Determine whether the improper integral
diverges or converges.
Evaluate the integral if it converges.
a.
b.
c.
diverges
531 Chapter 8: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
d.
e.
____ 12. Find the area between the x-axis and the graph of the function .
a.
b.
c.
d.
e.
____ 13. Suppose the capitalized cost C is given by where is the
original investment, t is the time in years, r is the annual interest rate compounded continuously, and
is the annual cost of maintenance. Find the capitalized cost C of an asset forever if
. Round your answer to the nearest dollar.
a.
b.
c.
d.
e.
8.8 Improper Integrals
532
____ 14. Suppose the capitalized cost C is given by where is the
original investment, t is the time in years, r is the annual interest rate compounded continuously, and
is the annual cost of maintenance. Find the capitalized cost C of an asset forever if
. Round your answer to the nearest dollar.
681,400
1,753,400
1,799,511
681,420
____ 15. Determine whether the improper integral diverges or converges. Evaluate the
integral if it converges.
3
2
1
diverges
533 Chapter 8: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8.8 Improper Integrals
Answer Section