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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Determine whether f'(0) exists.

f ( x ) = { x sin 1 x if x 0 0 if x = 0

To determine

Whether f(0) exits or not.

Explanation

Definition:

A function f(x) is differentiable at point x, then f(x)=limh0f(x+h)f(x)h.

Calculation:

Consider the function f(x)=xsin(1x) when x0 and f(0)=0,

By definition, f(x)=limh0f(x+h)f(x)h

Substitute x=0 in the above equation,

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