# Whether the statement “ If lim x → 6 [ f ( x ) g ( x ) ] exists, then the limit must be f ( 6 ) g ( 6 ) ” is true or true.

### 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 6RQ
To determine

Expert Solution

## Answer to Problem 6RQ

The statement “If limx6[f(x)g(x)] exists, then the limit must be f(6)g(6) ” is true.

### Explanation of Solution

Given information:

The given statement is “If limx6[f(x)g(x)] exists, then the limit must be f(6)g(6) ”.

Calculation:

Let consider that limx6[f(x)g(x)] is exists.

Consider f and g are two functions of x .

The product law of the limits is

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

The expression is

limx6[f(x)g(x)]

Apply the product law of the limits.

limx6[f(x)g(x)]=limx6f(x)limx6g(x)=f(6)g(6)

Therefore, the statement “If limx6[f(x)g(x)] exists, then the limit must be f(6)g(6) ” is true.

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