   Chapter 2, Problem 8RQ ### 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 neither lim x → a f ( x )   nor   lim x → a g ( x )   exists , then   lim x → a [ f ( x ) + g ( x ) ] does not exist.

To determine

Whether the statement, “if neither limxaf(x) nor limxag(x) exists, then limxa[f(x)+g(x)] does not exist” is true or false.

Explanation

The given statement is false since the below example disproves the given statement.

Let f(x)=1x2  and g(x)=1x2 and a=0.

Compute the limit of the functions as x approaches 0. That is, limx0(1x2) and limx0(1x2).

As x sufficiently close to 0 but x0, then the values of the functions f(x) and g(x) can be arbitrarily large.

Thus, the limit value of the functions does not exist.

Consider limxa[f(x)+g(x)]

limxa[f(x)+g(x)

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