Problem 13b

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. 13(a)]

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

By Ex. 13 (a) we have  

now  fourth order derivative is ;

Now the Interval is;