Chapter 2 - Limits - 2.3 Techniques for Computing Limits - 2.3 Exercises - Page 77: 37

$\displaystyle \lim_{x\rightarrow 0}|x|=0$

Approaching 0 from the negative side, $|x|$ approaches 0. $\displaystyle \lim_{x\rightarrow 0^{-}}|x|=0.$ Approaching 0 from the positive side, $|x|$ approaches 0. $\displaystyle \lim_{x\rightarrow 0^{+}}|x|=0.$ Since both one-sided limits exist and are equal to 0, the limit at zero exists, and $\displaystyle \lim_{x\rightarrow 0}|x|=0$