# Whether the statement “ If lim x → 0 f ( x ) = ∞ and lim x → 0 g ( x ) = ∞ , then lim x → 0 [ f ( x ) − g ( x ) ] = 0 ” 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 8RQ
To determine

## To find: Whether the statement “ If limx→0f(x)=∞ and limx→0g(x)=∞ , then limx→0[f(x)−g(x)]=0 ” is true or false.

Expert Solution

The statement “If limx0f(x)= and limx0g(x)= , then limx0[f(x)g(x)]=0 ” is false.

### Explanation of Solution

Given information:

The given statement is “If limx0f(x)= and limx0g(x)= , then limx0[f(x)g(x)]=0 ”.

Calculation:

The given statements are

limx0f(x)= and limx0g(x)= .

It does not mean that is a number nor does it mean that the limit exists. It expresses that the limit does not exist.

The notation limx0f(x)= and limx0g(x)= means that the values of f(x) and g(x) can be made arbitrarily large by taking x sufficiently close to 0 but not equal to 0

Therefore, the statement “If limx0f(x)= and limx0g(x)= , then limx0[f(x)g(x)]=0 ” is false.

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