Problem 42E

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 42E

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 , = = …………..(1)

By , using we get

= = 1 -2(-4x)+3

= 1 -2(-4x)+3, since ) if n is odd.

= 1 + 8x + 48

Therefore , the first four nonzero terms of the taylor series centered at ‘0’ for the function are 1+8 x + 48 .

That is , 1, x , 48 ,.

First term = 1

Second term = 8x

Third term = 48

Fourth term =