Day 12 (continued): Squeeze Theorem

My personal students have never respected the Squeeze Theorem, so that probably says a bit about my attitude when teaching it. I give them a bunch of those Squeeze Theorem questions where sine or cosine is being multiplied by usually some kind of monomial, and they're like, "these are stupid because answer is always zero - why do you even give us these problems?" Lol. They know, I promise, that DNE times zero isn't always zero, but it's just that those type of problems do work out to be zero.

Then there are those Squeeze Theorem questions that about what you can and cannot do with the Squeeze Theorem, like can this function be sandwiched between these other two functions? Why or why not? (Btw, the Squeeze Theorem is sometimes called the Sandwich Theorem just fyi). Anyway, those questions are usually pretty easy too if they understand how to play to with zero and infinity.

And finally, there is the third type of Squeeze Theorem question where they tell you that you have f(x) ≤ g(x) ≤ h(x) for some interval, and they want to know if the Squeeze Theorem can be used to find the limit of g(x) as x approaches a value (called a) in the aforementioned interval. These are not really fun either because they're just plug and chug problems. All you do pretty much is find f(a) and h(a) and see if they equal each other. If they do, great. You can find g(a). If f(a) ≠ h(a), then you cannot find lim x-->a of g(x).

I do show my students how the Squeeze Theorem can be used to find lim x-->0 of sin(x)/x but the problem is that since I show my students L'Hôpital early, they really just don't care. Maybe it's because I don't really care. I mean, it's kinda cool in its own right, but I could do without it. Thankfully, it's not very popular on the AP exam.

On block schedule, I don't spend a whole day on this. I teach this on the same day as piecewise functions, not that they have anything to do with each other.