Hi guys!

Someone in the tutoring center at my school asked me to do a limit problem for their calc 1 class, and I came up with the following solution. I would like someone to come up with an alternate solution, I don't really like mine, since I applied a theorem I believe to be true but don't recall ever seeing it done. I ended up with the right answer though, but I don't know if that was a coincidence.

Here's the "theorem" I used:

Theorem:If then . Provided and

Proof:Assume .

Then ..........since we are not dealing with infinite limits, the limit of the quotient is equal to the quotient of the limits (that's true right? )

Thus we have

QED

Now here's the question, and my solution.

Find

(Yeah, I know, you guys thought I'd have a much harder problem for you, well no, i'm only smart enough to tackle easy problems)

Solution:

....................

....................

....................

....................

Now recall that .

Applying the theorem I attempted to prove above we have that as well (This is the part I'm not sure about, I've never this limit defined as that before)

So,

Therefore

Can anyone come up with a better and/or shorter method? (L'Hopital's is not allowed).

Thanks