Numerically evaluating the limit of $\frac{x^4-1}{x^3-1}$ as $x\rightarrow 1$ What is the limit as $x \to 1$ of the function 
$$ f(x) = \frac{x^4-1}{x^3-1} . $$

Generally, the "numerical method" for finding limits involves substituting numbers closer and closer to the number and seeing if we get a pattern. 
In this example, we have $f(x)=\dfrac{x^4-1}{x^3-1}$. We should determine $f(1.1), f(1.01), f(0.99), f(1.001), f(0.999), \dots$ and see if a pattern develops. If these numbers approach some number, that would be our numerical estimate of the limit.
