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9.9 Representation of Functions by Power Series 563
9.9 Representation of Functions by Power Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find a geometric power series for the function centered at 0.
a.
b.
c.
d.
e.
____ 2. Find a geometric power series for the function centered at 0.
a.
b.
c.
d.
e.
564 Chapter 9: Infinite Series
____ 3. Find a geometric power series for the function centered at 0, (i) by the technique
shown in Examples 1 and 2 and (ii) by long division.
a.
b.
c.
d.
e.
____ 4. Find a power series for the function centered at 1.
a.
b.
c.
d.
e.
9.9 Representation of Functions by Power Series 565
____ 5. Find a power series for the function centered at 0.
a.
b.
c.
d.
e.
____ 6. Find a power series for the function centered at 0.
a.
b.
c.
d.
e.
566 Chapter 9: Infinite Series
____ 7. Find a power series for the function centered at 0.
a.
b.
c.
d.
e.
____ 8. Find a power series for the function centered at 0.
a.
b.
c.
d.
e.
9.9 Representation of Functions by Power Series 567
____ 9. Use the power series to determine a power series centered at 0
for the function .
a.
b.
c.
d.
e.
____ 10. Identify the interval of convergence of a power series .
a.
b.
c.
d.
e.
568 Chapter 9: Infinite Series
____ 11. Use the power series to determine a power series centered at 0
for the function .
.
a.
b.
c.
d.
e.
____ 12. Identify the interval of convergence of a power series .
a.
b.
c.
d.
e.
____ 13. Use the series for to approximate the value of
using . Round your answer to three decimal places.
a. 0.125
b. 0.111
c. 0.143
d. 0.100
e. 0.133
9.9 Representation of Functions by Power Series 569
____ 14. Use the power series to determine a power series for the
function .
a.
b.
c.
d.
e.
____ 15. Identify the interval of convergence of a power series .
a.
b.
c.
d.
e.
570 Chapter 9: Infinite Series
____ 16. Explain how to use the geometric series to find the
series for the function .
a. replace x with
b. replace x with and multiply the series by
c. replace x with and divide the series by 9
d. replace x with and divide the series by 9
e. replace x with
____ 17. Find the sum of the convergent series by using a well-known
function. Round your answer to four decimal places.
a. 0.1671
b. 0.7802
c. 2.4061
d. 0.0870
e. 2.3979
____ 18. Find the sum of the convergent series by using a well-
known function. Round your answer to four decimal places.
a. 0.1419
b. 0.2450
c. 0.8961
d. 0.1651
e. 0.1974
9.9 Representation of Functions by Power Series 571
9.9 Representation of Functions by Power Series
