# Order by asymptotic growth rate

1. Feb 18, 2012

### dba

1. The problem statement, all variables and given/known data
I try to order given functions and I am stuck with evaluating the following:

$f(n)= (n+1)!$ and $g(n)=n^{logn}$

2. Relevant equations
$\lim_{n\to\infty}\frac{f(n)}{g(n)} = 0$

then g(n) is faster growing.

$\lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty$

then f(n) is faster growing.

3. The attempt at a solution
I would guess that $n^{logn}$ is the faster growing function because it is exponential.
Thus, I write
$\lim_{n\to\infty}\frac{(n+1)!}{n^{logn}}$ and would expect the result to be zero.

My problem is that I do not know hot to take the limit of a factorial function and I also have a problem with the n^logn.
Can someone help me with this? Maybe I can write the functions in a different way?

Thanks for any help.

2. Feb 19, 2012

### Ninty64

Edit: Nevermind. Now I'm curious though.

[STRIKE]I might just be going out on a limb here, but I think that looking at it from this perspective might help:

By the definition of logarithm,
$log_{10}n = x$
implies
$n = 10^x$

I hope it helps at least[/STRIKE]