Calculus, find the limit, Exp vs Power? $\lim_{x\to\infty} \frac{e^x}{x^n}$
n is any natural number. 
Using L'hopital doesn't make much sense to me. I did find this in the book: 
"In a struggle between a power and an exp, the exp wins."
Can I refer that line as an answer? If the fraction would have been flipped, then the limit would be zero. But in this case I the limit is actually $\infty$

Let's consider the limit to infinity when taking log of that expression:
$$\lim_{x\rightarrow\infty} \ln{\frac{e^x}{x^n}} = \lim_{x\rightarrow\infty}x-n\ln(x)=\lim_{x\rightarrow\infty}x(1-\frac{n\ln(x)}{x})=\infty$$
Therefore, the limit is $\infty$.
The proof is complete.
