Problem 5E

Suppose you know the Maclaurin series for f and it converges for |x|<1. How do you find the Maclaurin series For f(x2)and where does it converge?

Solution 5E

Step 1:

In this problem we have to find the Maclaurin series for and where does it converge.

Given: Maclaurin series for f and it converges for |x|<1

The Maclaurin series is given by and it converges for

Now we have to find maclaurin series for

Replace by in the maclaurin series for