I was wondering if the following limit could be evaluated:
$$\lim_{x\to0}\left|\frac{\Gamma(x)}{\Gamma(-x)}\right|$$
I wondered if we could take the limit as $x$ approached $-1$ and compare the left and right side. I'm not even sure if this can be solved, and my knowledge on limits says it probably can't be solved.
But if you have an answer, you are welcome to give it a try.