BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 46E

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

Answer to Problem 46E

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

Find the value of the given limit in part (a) and (b) using graph.

Expert Solution

Explanation of Solution

Given:

The given limitsare limxxsin1x and limx0xsin1x .

Calculation:

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

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 3.3, Problem 46E

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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