   Chapter 2, Problem 9RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If lim x → a f ( x )   exists but   lim x → a g ( x )   does not exist , then   lim x → a [ f ( x ) + g ( x ) ] does not exist.

To determine

Whether the statement, “if limxaf(x) exists but limxag(x) does not exist, then limxa(f(x)+g(x)) does not exist” is true or false.

Explanation

Difference Law: Suppose that the limits limxaf(x) and limxag(x) exists, then

limxa[f(x)g(x)]=limxaf(x)limxag(x).

Calculation:

Given that, limxaf(x) exists but limxag(x) does not exist.

Suppose the limit f(x)+g(x) exists as x approaches a.

Take limxaf(x)=M and limxa(f(x)+g(x))=L.

Consider limxag(x)

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