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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 |f | is continuous at a, so is f.

To determine

Whether the statement, “if |f| is continuous at a, so is f continuous at a” is true or false.

Explanation

Consider the function f(x)=|x|x.

Evaluate the limit limx0f(x)=limx0|x|x as follows,

limx0f(x)=limx0|x|x=|0|0=00

Therefore, limx0f(x) is not defined. Hence, f(x) is not continuous at x=0

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