Greg, I'm guessing that's a well-known identity? I guess it doesn't require calculus, but I'd never come up with it in a million years.
Archie, it looks like your second term and mine are the same (if you "cancel out" the /dy bits).
I know historically, I'm going backwards, but we don't need to prove l'HÃ´pital's rule here; I know it works, so I'm using it.
And raven, yes, it doesn't make much sense to use l'HÃ´pital if you haven't learned derivatives yet.