Functions, Graphs, and Limits
Imagine our friend Moe has been dared, no, double dared. No. Triple Dog Dared. He must ride the dreaded spinning teacups in Disney World and then try to walk west toward Cinderella's Castle. Did we mention Moe can barely walk straight on a normal day?
Poor Moe survives the ride, but things are not looking good. He's looking a little green, but determined. We guide him to safety, then he's off. Moe starts in a generally southward direction but soon realizes the castle is out of sight. He changes course, over-corrects, and heads generally northward. He changes course again, over corrects, but is a little closer to being castle-bound by continuing on a southwest path. Imagine that this goes on for a really long time. Moe is getting closer and closer to walking completely west toward the castle. He may never walk perfectly west, but he'll at least get close.
Welcome to the wild world of limits. A world where we try to approach stuff: sometimes with a hit, sometimes with a miss.