I have two functions $f(n) = {(\log2) \over 100}n$ and $g(n) = 100\log(n)$. I am determining whether $f(n)$ is $\Omega(g(n))$, or equivalently, whether $g(n)$ is $O(f(n))$. To determine the latter, I am using L'Hôpital's rule on the expression $g(n)/f(n)$ to see whether $\lim_{x\to\infty} g(n)/f(n) = 0$, as this implies that for large values of $n$, $f(n)$ grows faster than $g(n)$.
Applying L'Hôpital's rule I have:
$\lim_{x\to\infty} g(n)/f(n) = \infty/\infty∞$, which is of indeterminate form
$\lim_{x\to\infty} g'(n)/f'(n) = {{(\log2) \over 100}\over100{1 \over n}} = {{(\log2) \over 100} \over 0}$, which is undefined.
Since $\lim_{x\to\infty} g'(n)/f'(n)$ is not defined, does this mean that $g(n)$ is not $O(f(n))$, and hence, $f(n)$ is not $\Omega(g(n))$?