   Chapter 11.10, Problem 84E

Chapter
Section
Textbook Problem

(a) Show that the function defined by f ( x ) = { e − 1 / x 2    if  x ≠ 0 0 if  x = 0 is not equal to its Maclaurin series.(b) Graph the function in part (a) and comment on its behavior near the origin.

To determine

(a)

To show:

The fx is not equal to its Maclaurin series

Explanation

1) Concept:

Maclaurin series of function  f

fx=n=0fn0n!xn

2) Given:

fx=e-1/x2  if x00           ifx=0

3) Calculation:

It is given that

fx=e-1/x2  if x00           ifx=0

We have to show fx is not equal to its Maclaurin series

So, to find Maclaurin series of fx

n=0fn0n!xn=f0+f'01!x+f''02!x2+

Find out f0, f'0, f''0,

Since f0=0, is given

f'0=limx0fx-f0x-0

To determine

(b)

To draw:

The graph of fx and then comment on its behaviour at the origin

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