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572 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 573
c.
d.
e.
____ 3. Use the definition to find the Taylor series centered at for the function
.
a.
b.
c.
d.
e.
574 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 575
____ 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.
576 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 577
____ 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.
578 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.
a. 0.81
b. 0.74
c. 0.89
d. 0.88
e. 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.
a. 0.1925
b. 0.1700
c. 0.1813
d. 0.1933
e. 0.1817
9.10 Taylor and Maclaurin Series 579
____ 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.
580 Chapter 9: Infinite Series
9.10 Taylor and Maclaurin Series
Answer Section
