Evaluate, hard limit problem.

Question

anonymous · Answer

$$ \lim_{x \rightarrow \infty} abs(\frac{ 1 }{ x! })^{1/x}$$

anonymous · Answer

@iPwnBunnies

anonymous · Answer

The answer solution says that the answer is 0, but I want to know how to do it.

accessdenied · Answer

My first observation is that, as it stands right now as x approaches infinity, we seem to get $0^0 $.  Do you agree with this assessment?
To fix that, we might like to use L'Hôpital's rule.  But to do that, we need to get it into a form like 0/0 or infinity/infinity, right?  Are you familiar with this sort of approach, or L'Hôpital's at all?

anonymous · Answer

I know l'hopitals but how do you get it to 0/0 or infinity/ infinity?

tkhunny · Answer

You may wish to introduce a logarithm.

anonymous · Answer

Okay thanks I need help with another problem right now.