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 2, Problem 5RQ
To determine

To find: Whether the statement “ If limx5f(x)=0 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist” is true or false.

Expert Solution

Answer to Problem 5RQ

The statement “ If limx5f(x)=0 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist” is false.

Explanation of Solution

Given information:

The given statement is “If limx5f(x)=0 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist”.

Calculation:

Let consider limx5f(x)=0 and limx5g(x)=0 .

Consider the two functions as

  f(x)=sin(x5)

  g(x)=x5

The expression is

  limx5[f(x)/g(x)]

Substitute the values in the above expression.

  limx5[f(x)/g(x)]=limx5sin(x5)x5=1

  limx5[f(x)/g(x)]=1 does exist hence the statement is false.

Therefore, the statement “ If limx5f(x)=0 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist” is false.

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