1. Section 11.3 – Power Series

3. THE RATIO TEST
10.3

5. 10.5

8. Find the radius of convergence of
Therefore, the radius of convergence is 3
Therefore, the radius of convergence is 1

9. Find the radius of convergence of
Therefore, the radius of convergence is infinite.

11. Find the Maclaurin series for
and determine its radius
of convergence
Radius of
Convergence
Is ½

12. The Taylor series about x = 0 for a certain function f converges
for all x in the interval of convergence. The nth derivative of
f at x = 1 is given by
a. Write the third degree Taylor polynomial for f about x = 0
b. Find the radius of convergence for the Taylor series about x = 0
Radius of Convergence is 3

13. The Taylor series about x = 0 for a certain function f converges
for all x in the interval of convergence. The nth derivative of
f at x = 1 is given by
a. Write the third degree Taylor polynomial for f about x = 0
b. Find the radius of convergence for the Taylor series about x = 0
Radius of Convergence
is infinite

14. Let f be the function defined by
a. Find for n = 1 to n = 3, where is the nth
derivative of f.
Write the first three nonzero terms and the general term
for the Taylor series expansion of f(x) about x = 1

15. Determine the radius of convergence for the series. Show
your reasoning
The radius of convergence is 1