Answer
$\lim\limits_{x \to 0} \vert x \vert = 0$
Work Step by Step
Let $\epsilon \gt 0$ be given.
Let $\delta = \epsilon$
If $\vert x-0 \vert \lt \delta$, then $\vert ~\vert x \vert - 0~\vert \lt \delta = \epsilon$
Therefore, $\lim\limits_{x \to 0} \vert x \vert = 0$
