   Chapter 2, Problem 26RQ ### 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 |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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