# Whether the statement “ If lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 , then lim x → 5 [ f ( x ) / g ( x ) ] does not exist” is true or false.

### 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 2, Problem 5RQ
To determine

## To find: Whether the statement “ If limx→5f(x)=0 and limx→5g(x)=0 , then limx→5[f(x)/g(x)] does not exist” is true or false.

Expert Solution

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.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!