Estimating Two-Sided Limits Numerically

Take the function $f(x)=\frac{3}{x-1}$ and solve for the following values to find $\lim\limits_{x\to1}{f(x)}$. $$\\\begin{array}{|c|c|c|} \hline 0&0.9&0.99&0.999&\rightarrow1\\ \hline &&&&\rightarrow?\\ \hline \end{array} \\\begin{array}{|c|c|c|} \hline 1\leftarrow&1.001&1.01&1.1&2\\ \hline ?\leftarrow&&&&\\ \hline \end{array}$$