Give the asymptotic complexity of each of the following functions in simplest terms. Then, order the functions by asymptotic dominance. In other words, give a sequence f_1, f_2, ... such that f_i = (n) = O (f_i+1 (n)). Make a note if any two functions are asymptotically equivalent, i.e. if f_i(n) = Theta (f_i+1 (n)) f_a (n) = lg(n^3) + lg(n^2) f_b (n) = 3^n+1 + 5n^4 f_c (n) = 3n^0.2 + 3n^0.8 f_d (n) = 2^16 f_e (n) = 41g (n^2 + 2n) + 6n^0.7 f_f (n) = n^5 + 2^n-2 f_g(n) = 3n lg(n^2 + 2) + n^2 f_h(n) = ((9n^2) (6n) (121))^1/2 f_i(n) = (4 + 5n + lg (n))^1/2 f_j(n) = lg^2 (n) + n lg (n^3) + 500 n f_k(n) = ((5n^5) (6n) (121n^1 0))^1/5 + n lg (n^1 00) f_l(n) = n^n-1 f_m(n) = 2^3 Squareroot n