# How do you find the largest interval #(c-r,c+r)# on which the Taylor Polynomial #p_n(x,c)# approximates a function #y=f(x)# to within a given error?

##### 1 Answer

Oct 6, 2014

Let us assume that there is

If we want the error to be less than

where

by replacing

By solving for

Hence,

I hope that this was helpful.