Hello, I would like to get help with the following question, thanks in advance.

Order the following functions according to their asymptotic growth rate. Justify the ordering.

n² --- n! --- (lg n)! --- (3/2)ⁿ --- ln ln n --- nlg(n) --- n2ⁿ ---- ln n --- eⁿ ---- n ---- sqrt(n) ---- 1

--- n^{(1/lg n)} --- ln²(n) --- 2ⁿ --- lg(n!)