Problem 1: (25 points) For each pair of functions in the list below, indicate their asymptotic relation (0,12, O). No justification is needed. . fi(n) = n, f2(n) = 2(log, n)10) fi(n) = n100, f2(n) = 2((log, n) 0) fi(n) = 101, fa(n) = 2(logan))) fi(n) = n, f2(n) = 2((log, n) 0.01) fi(n) = n100, f2(n) = 2((log, n)0:01) fi(n) = n.1, f2(n) = 2(log, n)0.01) . Problem 2: (25 points) Prove that in any tree with n vertices, the number of nodes with degree 8 or more is at most (n-1)/4