Another limit task, x over ln x, L'Hôpital won't do it?  $$\lim_{x\to 0 } \frac{x}{\ln x}.$$
This was wrong, I got a big red wrong! Why doesn't L'Hôpital work on this one? 
The problem is that $\ln$ is not defined for 0. It needs to be rewritten?
(Thanks to everyone helping me out with my homework, due anxiety I'm not able attend the class workshops.) 
Edit: I did get the correct limit ($0$), but that was a coincidence.

The limit, as written, does not exist because the function is not defined on an open neighborhood of the limit point: the function is not defined on $(-\infty,0)$, so you cannot take the limit as $x\to 0$. That would be a full answer.
If, however, the limit is taken only from the right, then the other answers you have received are correct: the limit is not an indeterminate form, it is equal to $0$. But you cannot get that by 'evaluating', because $\ln(x)$ is not defined at $0$.
