   Chapter 3.3, Problem 54E ### 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

# (a) Evaluate lim x → ∞   x sin 1 x . (b) Evaluate lim x → 0   x sin 1 x . (c) Illustrate parts (a) and (b) by graphing y = xsin( 1/x).

(a)

To determine

To evaluate: The value of limxxsin1x.

Explanation

Result used:

The limit of limx0sinxx=1

Calculation:

Compute limxxsin1x.

limxxsin1x=limx sin1x  1x

Substitute 1x for θ, then θ will approach to 0 as x approaches

(b)

To determine

To evaluate: The value of limx0xsin1x.

(c)

To determine

To sketch: The graph of the function y=xsin(1x).

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 