Estimating Two-Sided Limits Numerically

Take the function $f(x)=\frac{1}{x}-\frac{1}{|x|}$ and solve for the following values to find $\lim\limits_{x\to0}{f(x)}$. $$\\\begin{array}{|c|c|c|} \hline -1&-0.1&-0.01&-0.001&\rightarrow0\\ \hline &&&&\rightarrow?\\ \hline \end{array} \\\begin{array}{|c|c|c|} \hline 0\leftarrow&0.001&0.01&0.1&1\\ \hline ?\leftarrow&&&&\\ \hline \end{array}$$