H. Squeeze Theorem

Notice that x = 0 is not in the domain of this function. Nevertheless, we can look at the limit as xx approaches .0. From the graph we find that the limit is 1 (there is an open circle at x=0 indicating 0 is not in the domain).

We just convinced you this limit formula holds true based on the graph, but how does one attempt to prove this limit more formally? To do this we need to be quite clever, and to employ some indirect reasoning. The indirect reasoning is embodied in a theorem, frequently called the Squeeze Theorem.