Problem 18b

Given information

Here,  we have to use Taylor's Inequality to find the error ;

Taylor's Inequality is  stated as "If       for    , then the remainder     of Taylor series satisfies the Inequality 

.

Step-by-step explanation

By using the above mentioned information  and at and upto   the approximating Taylor's polynomial is;

              ]                [See the solution of Ex.18(a) ]

Here for using Taylor's Inequality first, have to calculate the fourth  order derivative of   .

BY ex.18(a) We have       

No the fourth order derivative :    .