Problem 43E

Working with binomial series Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Use the Taylor .series

Solution 43E

Step 1:

In this problem we need to find the first four nonzero terms of the Taylor series centered at 0 for the function by using the Taylor series

Consider

By using we get

Therefore the first four nonzero terms of the Taylor series centered at 0 for the function are . That is

First term

Second term

Third term

Fourth term