1. Section 11.3
Power Series

2. Find the Maclaurin Series for

3. Find the Maclaurin Series for

4. Find the Maclaurin Series for

5. Find the Maclaurin Series for

7. THE RATIO TEST
10.3

8. As before.

9. 10.5

10. converges for all x

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

13. Find the radius of convergence of
This is always true, so it converges for all x.
Therefore, the radius of convergence is infinite.

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

16. 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 = 0 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

17. 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 = 0 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

18. 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

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