Problem 62E

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 = 4; approximate .

Solution 62E

Step 1:

In this problem we need to find the coefficients for the Taylor series for the function 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 .