Chapter 1 - Limits and Their Properties - 1.2 Exercises - Page 58: 64

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -0.1 & -0.01 & - 0.001 & 0 & 0.001 & 0.01 & 0.1 \\ \hline f(x) & 2 & 2 & 2 & \text{undefined} & 2 & 2 & 2 \\ \hline \end{array}$$

Looking at the graph and table, we find that as $x$ approaches $0$ from the left and right, th function $f(x)$ approaches $2$. Thus, we can conclude that$$\lim_{x \to 0}\frac{|x+1|-|x-1|}{x}=2 .$$