Answer
$\lim\limits_{x\to0^+}\Big(\frac{1}{x}-\frac{1}{|x|}\Big)=0$
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,
$A=\lim\limits_{x\to0^+}\Big(\frac{1}{x}-\frac{1}{x}\Big)$
$A=\lim\limits_{x\to0^+}0$
$A=0$
