4 Dec 2021
Problem 16b
Page 626
Section 8.8: Application of Taylor Polynomials
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
4 Dec 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. 15(a)]
Here for using Taylor's Inequality first, have to calculate the fourth order derivative of .
By Ex. 16 (a) we have
and fourth order derivative is