Problem 17b

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.17(a)]

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

By,Ex.17(a) we have      

Now fifth order derivative :   

Since the given interval is