I need proofs for each one (i.e. take the limit as n->infinity) with one expression in the numerator and one in the denominator.

5) Rearrange the following functions as needed so that they are listed from left to right in increasing order of growth: (n 2)! , 5 lg(n + 100)10, 221, 0.001n* + 3n3 +1 , In?(n), Vn , zn