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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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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