Alternative approach Compute the coefficients for the Taylor series for the following functions about the given point a and then use the first four terms of the series to approximate the given number.

with a = 16; approximate .

Solution 63E

Step 1:

In this problem we need to find the coefficients for the Taylor series for the function with and then we have to approximate

The -order Taylor polynomial for y = f(x) at is:

It can also be written in sigma notation as follows,

where the constants is the Taylor coefficient of about .

Step 2:

We have with

Thus the Taylor coefficients for with is

Few coefficients are given below,