Explanation Given: f ( x ) = | x | . Here we have to prove that lim x → 0 f ( x ) = 0 . This can be proved by taking the Left Hand Limit and Right Hand Limit for the given function. We know that if a limit exists for a function then its Left Hand Limit and Right Hand Limit should be equal. If they are not equal, then the limit does not exist. The given function f ( x ) = | x | implies that for x ≥ 0 , then f ( x ) = x andfor x < 0 , then f ( x ) = − x . Calculation: Description: Step 1 : Find the Right Hand Limit for the given function f ( x ) = | x |

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 2.9, Problem 26E

To determine

The proof rigorously that limx→0f(x)=0 for the given function f(x)

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Chapter 2.9, Problem 25E

Chapter 2.9, Problem 27E

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Chapter 2 Solutions

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The proof rigorously that lim x → 0 f ( x ) = 0 for the given function f ( x )

Solution Summary: The author explains how to prove that undersetxto 0mathrmlimf(x)=0 exists for the given function.

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The proof rigorously that limx→0f(x)=0 for the given function f(x)

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Chapter 2 Solutions