Answer
$0$
Work Step by Step
With $x\to 0^+$, we have $x\gt0$ and $|x|=x$, thus
$$\lim_{x\to 0^+}(\frac{1}{x}-\frac{1}{|x|} )=\lim_{x\to 0^+}(\frac{1}{x}-\frac{1}{x})=\lim_{x\to 0^+}(0)=0$$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 13 - Section 13.2 - Finding Limits Algebraically - 13.2 Exercises - Page 913: 42
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