(a) Find the best possible relationship using one of the notations: O, , , o, , for the following pairs of functions: n ³ + 7n ^1.5 3 and n^log8 10n^0.5 + 7; nlgn and n ^1.1 ; 5ⁿ and (5.1)ⁿ ; 4ⁿ and n!. Justify each answer.

(b) Function f(n) = n ³ + 5000n 60000 when n 50 and f(n) = nlog n + 100n for n > 50. Write f(n) in asymptotic notation in the simplest possible form.

Please provide with good explanation.