# Whether the statement “ If lim x → 5 f ( x ) = 2 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 4RQ
To determine

## To find: Whether the statement “ If limx→5f(x)=2 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)=2 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist” is true.

### Explanation of Solution

Given information:

The given statement is “If limx5f(x)=2 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist”.

Calculation:

Let consider limx5f(x)=2 and limx5g(x)=0 . And f and g are two functions of x .

The quotient law of limits is

limxa(fg)(x)=limxaf(x)limxag(x)

Here, the limxag(x)0

Apply the quotient law of limits on limx5[f(x)/g(x)] .

limx5[f(x)g(x)]=limxaf(x)limxag(x)

Since, the limxag(x)0 hence limx5[f(x)/g(x)] does not exist.

Therefore, the statement “ If limx5f(x)=2 and limx5g(x)=0 , then limx5[f(x)/g(x)] does not exist” is true.

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