   Chapter 11.10, Problem 44E

Chapter
Section
Textbook Problem

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f ( x ) = { x − sin x x 3  if  x ≠ 0 1 6             if  x = 0

To determine

To obtain:

The Maclaurin series for the given function.

Explanation

1) Concept:

The Maclaurin series for the function sinx=n=0(-1)n(x)2n+1(2n+1)!=x-x33!+x55!-x77!+, R=

2) Given:

3) Calculation:

Consider the given function.

For  x0

fx=x-sinxx3

The Maclaurin series for the function  sinx  is

n=0(-1)n(x)2n+1(2n+1)!=x-x33!+x55!-x77!+

Subtracting the Maclaurin series for the function  sinx  from  x,  get the Maclaurin series for function

x- sinx,

=x-n=0(-1)n(x)2n+1(2n+1)!

Dividing the Maclaurin series for the function x- sinx by x3,   get the Maclaurin series for the function

x-sinxx3,

=1x3x-n=0-1nx2n+12n+1!

Substituting,

n=0(-<

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