Originally Posted by

**beebe** So I have the answer to this problem, and I know it's correct, but I want to be sure that the moves I made were legal to get there. Here's the problem:

$\displaystyle \lim_{x\to\infty}e^{x^2-x}$

Here's what I did:

$\displaystyle =\frac{lim_{x\to\infty}e^{x^2}}{lim_{x\to\infty}e^ x}$$\displaystyle =\frac{e^{lim_{x\to\infty}x^2}}{e^{lim_{x\to\infty }x}}$$\displaystyle =\frac{e^1}{e^1}=1$

Were all my moves legal? Specifically, moving the limit sign up into the exponent. Is there a rule that let's me say $\displaystyle \lim_{x \to a}B^x=B^{\lim_{x \to a}x}$ ?