Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 46

Answer

0

Work Step by Step

$|x|=\left\{\begin{array}{lll} x & if & x \geq 0\\ -x & if & x < 0 \end{array}\right.$ Approaching $x=0$ from the right, means $x > 0$... so, $\displaystyle \lim_{x\rightarrow 0+}(\frac{1}{x}-\frac{1}{|x|})=\lim_{x\rightarrow 0+}(\frac{1}{x}-\frac{1}{x})=\lim_{x\rightarrow 0+}0=0$.
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