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Chapter 1: Q40P (page 32)

f(x)=1x,a=1

Short Answer

Expert verified

1x=1-(x-1)+(x-1)2-(x-1)3+鈥�

Step by step solution

01

Given information

The Maclaurin expansion of the function f(x)=1x,a=1is to be evaluated.

02

Definition of Maclaurin series

The definition of the Maclaurin series is defined.

11+x=1-x+x2-x3+鈥�

03

Begin by stating the Maclaurin series

State the Maclaurin series.

f(x)=1x=11+(x-1)11+x=1-x+x2-x3+鈥�

04

Make appropriate substitution in the Maclaurin series and evaluate

Replace xwith the expression (x-1)in the third defined Maclaurin series.

11+(x-1)=1-(x-1)+(x-1)2-(x-1)3+鈥�

1x=1-(x-1)+(x-1)2-(x-1)3+鈥�

Thus, the final answer is1x=1-(x-1)+(x-1)2-(x-1)3+鈥�

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Most popular questions from this chapter

f(x)=sin鈥�x,鈥�a=蟺/2

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