Limits and Continuity: $\lim\limits_{n\to\infty}e^{\frac{1}{n}}$ Well, I'm doing this and I already find a resolution. I can write that limit as:
$e^{\lim\limits_{n\to\infty}\frac{1}{n}}$ and that results in $1$. 


  My question is: Why can I do this?
A function $f(x)$, is continuous at a point, $a$ if:

$$\lim\limits_{x\to a} f(x) = f(a)$$

This is the definition of continuity. So if $n\to \infty$, then $\frac1n \to 0$, so:

$$\lim\limits_{n\to\infty} e^{1/n}=\lim\limits_{x\to 0} e^x=e^0=1$$

because $e^x$ is continuous at $0$.
You can do it because when $n$ gets really big $ \frac{1}{n}$ is going to get really close to zero, and anything to the zeroth power is always one. $e^{0} = 1$. I'm not sure if that answers your question though.

Jeez, constant downvotes. Anyone care to tell me what I did wrong?