## Calculus 8th Edition

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