19 Nov 2021
Problem 22
Page 626
Section 8.8: Application of Taylor Polynomials
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
19 Nov 2021
Given information
We have a function whose Maclaurin series expansion is ;
.......................................(1)
Here we use Taylor's Inequality which states that " If for , then the
remainder of the Taylor series satisfies the inequality -
" .
Step-by-step explanation
Step 1.
Here a=0 in equation (1) ,so that Taylor series becomes Maclaurin's series and we apply Taylor Inequality theorem on the given function.
In this problem we have to find n for which .
Since , the given series in equation (1) is alternating series , so by Alternating Series Estimation Theorem ."The error in approximating by first n terms
is atmost .