Problem 1 (4 points). Given the following functions, give the tightest upper bound for the functions using big-O asymptotic notation. a) T(n) = 500n + n 1.4 b) f(n) = 1.45 + Vn4 c) g(n) = n*.logs (n) + nyn? d)t(n) = 2"log(n) + n'-log(n) Problem 2 (10 points). For the two given functions f(n) and g(n) below, show that fin) is asymptotically smaller than g(n). f(n)= nyn5(log(n))* g(n)= 13.6