Problem 22

Given information

We have a function whose Maclaurin series expansion is ;

          .......................................(1)

Here we  use Taylor's Inequality which states that " If         for    , then the

remainder   of the Taylor series satisfies the inequality -

" .

Step-by-step explanation

Here a=0  in equation (1) ,so that Taylor series becomes Maclaurin's series  and we apply Taylor Inequality theorem on the given function.

In this problem we have to find  n for which .

Since , the given series in equation (1) is alternating series , so by Alternating Series Estimation Theorem ."The error in approximating   by first n terms

is atmost        .