Day 8: Limits of Compositions

If I were teaching on block schedule, I would probably include this lesson with the previous lesson. It's a pretty short concept to understand as far as I know.

When I first started teaching calculus, I used a textbook for the whole curriculum. And Limits of Compositions was definitely not a lesson on its own in the textbook. There are probably a couple of these thrown into the book somewhere, and so I didn't pay much attention to it.

Then one day, I got a problem wrong. It went something like this:

I thought the answer was DNE since the limit of f(x) at x = -1 didn't exist. But then I learned that since g(x) ≥ -1 @ x = 2, we only care about the values that are MORE than -1, meaning when you do the limit of f(x), you only do it from the right hand side of -1. I don't know if that's ever been on AP exam, but I know that there are a couple of problems like this in AP Classroom.

If I were teaching on a 45 minute class length, I'd probably do one-sided limits along with this concept.