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Working with binomial series Use properties of | Ch 9.3 - 42E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 42E Chapter 9.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 42E

Problem 42E

Working with binomial series Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Use the Taylor .series

Step-by-Step Solution:

Solution 42E

Step 1:

In this problem we need to find the first four nonzero terms  of the taylor series centered at ‘0’ for the function  = by using the taylor series :

Consider ,  = = …………..(1)

By , using we get

= = 1 -2(-4x)+3

                                    = 1 -2(-4x)+3, since ) if n is odd.

                                   = 1 + 8x + 48

Therefore , the first four nonzero terms of the taylor series centered at ‘0’ for the function   are 1+8 x + 48 .

That is ,  1, x , 48 ,.

First term = 1

Second term = 8x

Third term = 48

Fourth term =

Step 2 of 1

Chapter 9.3, Problem 42E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Working with binomial series Use properties of | Ch 9.3 - 42E