8.5 Partial Functions 479
8.5 Partial Functions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
____ 2. Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
480 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 3. Write the form of the partial fraction decomposition for the following rational
expression.
a.
b.
c.
d.
e.
____ 4. Use partial fractions to find .
a.
b.
c.
d.
e.
8.5 Partial Functions 481
____ 5. Use partial fractions to find the integral .
a.
b.
c.
d.
e.
____ 6. Use partial fractions to find the integral .
a.
b.
c.
d.
e.
____ 7. Use partial fractions to find
a.
b.
c.
482 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
d.
e.
____ 8. Use partial fractions to find the integral
a.
b.
c.
d.
e.
____ 9. Use partial fractions to find .
a.
(1/
5
)arctan(x/
5
)
b.
c.
(1/
5
)arcsin(x/
5
)+C
d.
e.
arctan(x/
10
)
8.5 Partial Functions 483
____ 10. Evaluate the definite integral .
a.
b.
c.
d.
e.
____ 11. Use substitution to find the integral .
a.
b.
c.
484 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
d.
e.
____ 12. The predicted cost C (in hundreds of thousands of dollars) for a company to remove
p% of a chemical from its waste water is shown in the table below. A model for the data is given by
. Use the model to find the average cost for removing between
75% and 80% of the chemical.
p 0 10 20 30 40 50 60 70 80 90
C 0 0.6 1 1.3 1.6 2 2.6 3.5 5.3 10.3
a. $470,000
b. $235,000
c. $117,500
d. $470,001
e. $940,000
____ 13. Evaluate the definite integral
.
a.
b.
c.
d.
e.
8.5 Partial Functions 485
____ 14. Use substitution and partial fractions to find the indefinite integral.
.
a.
b.
c.
d.
e.
____ 15. Find the area of the region bounded by the graphs of , y = 0, x = 0,
and x = 1.
a. A =
b. A =
c. A =
d. A =
e. A =
486 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.5 Partial Functions
Answer Section