Section 1.2 - Formal Limits
Our heuristic definition of a limit involved a lot of vague words like "close to" or "approaches". In this section, we're going to make the definition more mathematically precise then see how we can use that definition to derive properties of limits some of which we hinted at in the last section's Explorations questions.
Videos
Lectures
Now that we have a solid idea of what a limit should look like, we're in a position where we can come up with a formal, mathematical definition. (lecture slides)
Now that we have our precise definition, let's take it out and see how it handles some specific examples. (lecture slides)
This is the first of the really theoretical lectures in the course. We start with a couple of small but useful theorems then look at a list of properties. I'll prove both of the theorems and a couple of the properties then leave the rest as exercises. If you aren't so much interested in the proving side of things, you can listen to the descriptions and then skip ahead when I start talking about epsilons and deltas. (lecture slides)
