Find the value of thegiven limit .

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.3, Problem 46E

a.

To determine

Find the value of thegiven limit .

Expert Solution

The limxxsin1x=1 .

Explanation of Solution

Given:

The given limitis limxxsin1x .

Calculation:

limxxsin1x

Let x=1t .

If 1t , then t0 .

limxxsin1x=limt01tsint

Use limit formula limx0sinxx=1 .

=1

Hence the value of the limxxsin1x=1 .

b.

To determine

Find the value of the given limit .

Expert Solution

The limx0xsin1x=0 .

Explanation of Solution

Given:

The given limitis limx0xsin1x .

Calculation:

limx0xsin1x

Let x=1t .

If 1t0 , then t .

limx0xsin1x=limt1tsint

From Squeeze theorem limxsinxx=0 .

=0

Hence the value of the limx0xsin1x=0 .

c.

To determine

Expert Solution

Explanation of Solution

Given:

The given limitsare limxxsin1x and limx0xsin1x .

Calculation:

Graph of the function y=xsin(1x) is given below.

From the graph,

When x , then the value of the limxxsin1x=1 .

When x0 , then the value of the limx0xsin1x=0 .

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