I'm retaking Calculus I right now during the summer. It's been quite a while but I am pretty much breezing through it except for the limit section. I remember the first time around, my prof didn't put ANY emphasis on limits and I haven't really had to do much of anything with limits since then during my math degree. This prof I have now however, seems to love them. Radicalizing, substitution, factoring them; whatever. My question is this: I noticed that pretty much any limit he's given me I am able to pretty much take the lazy way out and just do L'Hospitals rule for it and it comes out with the same answer whether its an infinite or finite limit. I won't even begin to pretend I know much about limits but is there a specific time in which I CAN'T do L'Hospitals? Obviously if I look at a single limit like (×-1)^2 i'm not going to start using chain rule on it, but what are my restrictions?