Problem 21

Given information

We have   a function whose Maclaurin series expansion is as follows;

          ..........................(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 in the given  function.

In this problem we have to find such n for which .

Since ,

And ,

At x=0.1 ,    ,