Problem 23

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 three terms and the next term will be fifth , and  all even terms are zero  . So we have to take n=4 in Taylor's Inequality .

Step-by-step explanation

Now,

 first derivative ,

 
second derivative ,  

third derivative ,

fourth derivative

and fifth order derivative ,

Now,