Please do ALL parts.

Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2 (n)) (b) 2^n elementof O(n!) (c) log_2 (n^2) + log_2 (100n^10) elementof O(log_2 (n)) d) n^1/2 middot O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n^2)