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: 46



Work Step by Step

$A=\lim\limits_{x\to0^+}\Big(\frac{1}{x}-\frac{1}{|x|}\Big)$ In this case, we consider $x\to0^+$, which means we only consider the values of $x\gt0$. While we know that, $$|x|=x\hspace{.5cm}for\hspace{.5cm}x\geq0$$ Therefore, $A=\lim\limits_{x\to0^+}\Big(\frac{1}{x}-\frac{1}{x}\Big)$ $A=\lim\limits_{x\to0^+}0$ $A=0$
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