help me solve this!!

Order the following functions by growth rate: N N NS. NP, Nlog N. Nlog log N, N log' N. N log(N). 2/N, 2N 2N/2.37. N logN, N. Indicate which functions grow at the same rate. Suppose T(N) = O(N)) and T (N) = O(f(N)). Which of the following are true? a. T (N) + T2(N) = O((N)) b. T.(N) - T2(N) = o((N)) T(N) T2(N) = 0(1) d. Ti(N) =0(T2(N)) Prove that for any constant k, log" N = o(N). Find two functions f(N) and g(N) such that neither (N) = O(g(Nnor g(N) = O(f(n)). 5) For the following program fragment: Give an analysis of the running time (Big-Oh will do)