   Chapter 2, Problem 9P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If lim x → a [ f ( x ) + g ( x ) ] = 2   a n d   lim x → a [ f ( x ) − g ( x ) ] = 1 , find lim x → a [ f ( x ) g ( x ) ] .

To determine

To find: The value of the limit of the function limxa[f(x)g(x)].

Explanation

Result used:

Sum law: limxa[f(x)+g(x)]=limxa[f(x)]+limxa[g(x)]

Difference law: limxa[f(x)g(x)]=limxa[f(x)]limxa[g(x)]

Product law: limxa[f(x)g(x)]=limxa[f(x)]limxa[g(x)].

Calculation:

Obtain the limit of the function f(x)g(x) as x approaches a.

Suppose limxa[f(x)+g(x)]=2 and limxa[f(x)g(x)]=1.

Consider limxa[f(x)+g(x)]=2.

limxa[f(x)+g(x)]=2limxa[f(x)]+limxag(x)=2[by Sum Law]

Thus, limxa[f(x)]+limxag(x)=2. (1)

Consider limxa[f(x)g(x)]=1.

limxa[f(x)g(x)]=1limxa[f(x)]limxag(x)=1[by Difference Law]

Thus, limxa[f(x)]+limxag(x)=2

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