Mooculus 2: Infinity and continuity
15 videos • 22,795 views • by Jim Fowler Week 2 starts by digging deeper into limits by studying one-sided limits. Next, we study continuity: continuity makes precise the idea that small changes in the input don't affect the output too much. Many of the functions we think about are continuous: for instance, polynomials are continuous. And we'll be considering continuity more in the weeks to come. Once we know the basics of continuity, we study the intermediate value theorem, and apply the theorem to two problems: one that approximates a square root, and another that finds a fixed point. Limits provide one way to make ponderings about infinity precise. To see how limits handle infinity, we observe that "infinity" may play a role in the output or in the input: when the output of a function is as large as we like, we might say "the limit equals infinity;" when the input is large, we may ask about "the limit of f(x) as x approaches infinity." Sometimes people are tempted to do calculations with infinity as if it were a number, but remember that infinity is not a number so you cannot expect "calculations" like "infinity divided by infinity" to be meaningful. If you want to dig into the definitions, the week ends with three bonus videos for you. Those last three videos should be skipped if you aren't enjoying them, since it won't be needed at all for what follows in the course.