Question 1 [30 Points] For each pair of functions below, first determine which function grows asymptotically faster, and then express the relation between the two functions using all the asymptotic notations (, O, Q, o and u) that apply. Only give the relations in which f(n) appears on the left-hand side. Prove the relation between the first two pairs of functions using the limit definition. (1) f(n) = n logn (2) f(n) = 2n (3) f(n) = 3n (4) f(n) = 6n3+7n2+2 (5) f(n) = n50 g(n) = n + logn g(n) = 22n g(n) = 3m2 g(n) = n3 g(n) = n