Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises - Page 103: 45


Limit does not exist

Work Step by Step

$x\lt 0$ so $|x|=-x$ $\lim\limits_{x \to 0^-}(\frac{1}{x}-\frac{1}{|x|})=\lim\limits_{x \to 0^-}(\frac{1}{x}-\frac{1}{-x})=\lim\limits_{x \to 0^-}\frac{2}{x}=-\infty$ $\therefore$ limit does not exist.
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