Answer
$$\lim_{x\to 1} f(x)= 1.5 $$
Work Step by Step
Given $$f(x)=\frac{x^{3}-1}{x^{2}-1} $$
\begin{array}{|c|c|c|c|}
\hline
x & f(x) & x & f(x) \\ \hline
1.002 & 1.5015005 & 0.998 & 1.498500501 \\ \hline
1.001 & 1.500750125 & 0.999 & 1.499250125 \\ \hline
1.0005 & 1.500375031 & 0.9995 & 1.499625031 \\ \hline
1.00001 & 1.5000075 & 0.99999 & 1.4999925 \\ \hline
\end{array}
Then from the table, we get:
$$\lim_{x\to 1} f(x)= 1.5 $$
