Which function is faster $f_1$ or $f_2$

Question

I'm trying to compare two functions asymptotically, are there any simple solution for this?

$f_1(n) = 3n^2 + {\dfrac{100\log n}{\sqrt n}} $

$f_2(n) = 10 + \dfrac{2(n! - 5n)}{n^{3/2}} $

Which one is better?

Answer 1

Please show some of your work or an attempted solution. One hint I can give you is to look up and use Sterling's approximation for the factorial.