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 .
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 .
We have with
Thus the Taylor coefficients for with is
Few coefficients are given below,