# The value of lim x → a f ( x ) g ( x ) . ### 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 15P
To determine

## To find:The value of limx→af(x)g(x) .

Expert Solution

The value of limxaf(x)g(x) is 34 .

### Explanation of Solution

Given information:

The given equations are limxa[f(x)+g(x)]=2 and limxa[f(x)g(x)]=1 .

Calculation:

Consider that, f(x) and g(x) are two functions as given limxa[f(x)+g(x)]=2 and limxa[f(x)g(x)]=1 .

Calculate the f(x)g(x) .

f(x)g(x)=14{[f(x)+g(x)]2[f(x)g(x)]2}

Take limits on both sides.

limxaf(x)g(x)=limxa14{[f(x)+g(x)]2[f(x)g(x)]2}limxaf(x)g(x)=14{limxa[f(x)+g(x)]2limxa[f(x)g(x)]2}=14{2212}=34

Therefore, the value of limxaf(x)g(x) is 34 .

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