I was out the day we went over L’Hopital’s rule in Calc II, and my sub covered it. (Yay for subs who can teach Calc II!)
When I came back, my student asked me, “So, why does L’Hospital’s Rule work?” So we proved it – at least the 0/0 case, which was all I had in my notes.
“Ok, so why does the infinity/infinity case work?” (I love that she asks these questions!)
“Hmm…” I answered as I stared at it. “Maybe because…uhm….hmmm. I’m not sure. Can I think about that and get back to you?”
I had to look it up, but today I got back and proved it. And she still wanted to know!
Next time, hopefully, I’ll be there, and we’ll prove both that day. But I should add these to my notes.