for question 2 lg is log base 2 and ln is log base e (natural log)

2. Order the following functions according to their asymptotic growth rate. Justify the ordering. n2 n! (1g n)! (3/2)* In Inn nlg(n) n21 inn en n sqrt(n) 1 (11gn) In?(n) 24 1g(n!) 3. Suppose T(n) = O(f(n)) and R(n) = (g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1. 1. Prove that: T(n) +R(n) = of f(n) + g(n)) 2. Prove that T(n)*R(n) = O( f(n)*g(n)) 3. Disprove the claim that T(n)/R(n) = 0( f(n)/g)), i.e., provide a counter example