Problem 24

Given information

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

remainder      of the Taylor series satisfies the inequality -

Since the Series  only contain four  terms and the next term will be sixth , and  all odd degree  terms of x are zero  . So we have to take n=5 in Taylor's Inequality.

Step-by-step explanation

Now ,  

first derivative ;

second order derivative ;

third order derivative ;

fourth order derivative ;

fifth order derivative ;

& sixth order derivative is;