Kinda weird how little I could glean about this one on the webernet. Oh, there were TONS of other examples, but this one is, uhh, too simple? Maybe?

I know that the answer is

. I know multiple ways to figure out the answer. My question to you is if I can use l'Hopital's rule on it?

If you use it without factoring first, you get

OR

which will tend to

as

. But if you factor first, you get

. Now from here you can just say it's

and be done with it, but I don't think that holds up to a math teacher (does it?) so IF I continue and get derivatives then it becomes

which can be written as

.

Intuitively this SEEMS to make sense, but am I missing something? I don't want to demonstrate this only to lose points for not seeing that l'hopital's rule doesn't apply. Can someone show me the light?

Thanks!