Help with finding Limit What is the limit  of  $$\lim_{n \to \infty} \left(\frac{n!}{n^n}\right)^{\frac{3n^3+4}{4n^4-1}}$$
Does any one can help, I am not sure how to solve this.

hint: Use the famous Sterling inequality:  
$$ \sqrt{2\pi n}\left(\dfrac{n}{e}\right)^n \le n! \le \sqrt{2\pi n}\left(\dfrac{n}{e}\right)^n\cdot e^{\frac{1}{12n}}$$
 and use the Squeeze lemma to find the limit. Can you manage to take it from here?
