Finding a tricky limit two ways

Suppose you're asked to find or . This is a tricky limit to take because:

One way to evaluate these limits is to graph the rational function (or perform the analogous algebraic technique to determine the location of the holes in question).

But there is another approach too. Experiment with the applet below.

This applet illustrates an application of:

Check all that apply

In the applet above and are only approximately equal near and , but not otherwise. This serves as a reminder that: