24 Nov 2021
Problem 14b
Page 626
Section 8.8: Application of Taylor Polynomials
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
24 Nov 2021
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
Step 1.
By using the above mentioned information and at and upto the approximating Taylor's polynomial is;
[See the solution of Ex. 14(a)]
Here for using Taylor's Inequality first, have to calculate the fifth order derivative of .
By Ex. 14 (a) we have
Now fifth order derivative is ;
Now the Interval is;