Jameson, your problem, informally was that you looked at the exponent you should have also seen the base thus it is of the form $\infty^0$ no conclusion could be drawn.
Alright. I admit I didn't post a formal argument. I realize $\infty^0$ doesn't express a limit, but like I said before, I was trying to be analytical as I knew what the limit was. I like both of your reasonings.