Is there a faster way to solve this limit, other than using L'Hopital's Rule twice?
I agree with Jhevon, and it is also more interesting if you try to avoid using L' Hôpital.
A bit about Taylor polynomials: the nth degree polynomial of , , centered in , let's say "a", has the following property: , ... .
It turns out to be a good approximation of the function (in a certain interval)
The remainder is given by for some
You can check that:
Look it up in your calculus book, it should have something about this