   Chapter 2.7, Problem 60E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Determine whether f'(0) exists. f ( x ) = { x 2 sin 1 x   if   x ≠ 0 0       if   x = 0

To determine

Whether f(0) exits or not.

Explanation

Squeeze theorem:

Suppose an inequality of functions g(x)f(x)h(x) in a interval around c and that limxcg(x)=L=limxch(x). Then limxcf(x)=L.

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)=x2sin(1x) when x0 and f(0)=0,

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

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