The link provides you with a pretty powerful limit calculator. Not only does the calculator give you the limit, it also shows you how to calculate it. The calculator may use a technique that we have not covered yet, but enjoy anyway!
Go here for a detailed explanation on how to graph piecewise functions on a TI-83 or -84. Note the instruction to change your "mode" from "CONNECTED" to "DOT." I believe on the most recent OS update for TI-84, you don't have to do this step.