591
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
592
____ 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.
593
Chapter 9: Infinite Series
____
7.
Find a power series for the function
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
594
____ 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.
595 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.
0.125
0.111
0.143
0.100
0.133
9.9 Representation of Functions by Power Series
596
____
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.
597 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.
0.1671
0.7802
2.4061
0.0870
2.3979
____ 18. Find the sum of the convergent series by using a
well-known function. Round your answer to four decimal places.
0.1419
0.2450
0.8961
0.1651
0.1974
9.9 Representation of Functions by Power Series
598
9.9 Representation of Functions by Power
Series Answer Section
599 Chapter 9: Infinite Series
9.10 Taylor and Maclaurin Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the definition to find the Taylor series (centered at c) for the function.
a.
b.
c.
d.
e.
____ 2. Use the definition to find the Taylor series centered at for the function
.
a.
b.
9.10 Taylor and Maclaurin Series
600
c.
d.
e.
____ 3. Use the definition to find the Taylor series centered at for the function
.
a.
b.
c.
d.
e.
601
Chapter 9: Infinite Series
____
4.
Use the definition to find the Taylor series (centered at c) for the function.
a.
b.
c.
d.
e.
____
5.
Use the definition to find the Taylor series centered at
for the function
.
a.
b.
c.
d.
e.
9.10 Taylor and Maclaurin Series
602
____
6.
Use the binomial series to find the Maclaurin series for the function
.
a.
b.
c.
d.
e.
____
7.
Use the binomial series to find the Maclaurin series for the function
.
a.
b.
c.
d.
e.
603 Chapter 9: Infinite Series
____ 8. Use the binomial series to find the Maclaurin series for the function.
a.
b.
c.
d.
e.
9.10 Taylor and Maclaurin Series
604
____
9.
Find the Maclaurin series for the function
.
a.
b.
c.
d.
e.
____
10.
Find the Maclaurin series for the function
.
a.
b.
c.
d.
e.
605
Chapter 9: Infinite Series
____
11.
Find the Maclaurin series for the function
.
a.
b.
c.
d.
e.
____ 12. Use a power series to approximate the value of the integral with an error of
less than 0.01. Round your answer to two decimal places.
0.81
0.74
0.89
0.88
0.84
____ 13. Use a power series to approximate the value of the integral with an
error less than 0.001. Round your answer to four decimal places.
0.1925
0.1700
0.1813
0.1933
0.1817
9.10 Taylor and Maclaurin Series
606
____ 14.
Evaluate
using the formula
where
k is a real number, n is a positive integer, and
.
a.
31
b.
45
c.
56
d.
21
e.
35
____ 15. Use the definition to find the Taylor series centered at for the function
.
a.
b.
c.
d.
e.
607 Chapter 9: Infinite Series
9.10 Taylor and Maclaurin Series
Answer Section