a. (4 points) Show that for any constants a and b, a, b > 0, (n + a)-(nb). b. Arrange the following functions in ascending order of growth rate so that each function is big-0 of the next function. bl. (2 points) n25, v2n, n + 10, 10", 100", n2 log n 62. (2 points) n5, (logn)2, n1.0001, (1.0001)", 2, n(log n)1001, n (log n)10000 63. (2 points) 2100m, 22, n", nlogn, n log n log log n, n3/2, n(logn)s/2, n4/3(logn)2 (HINT: Use the fact that logbn-O(n*) for all constants b > 1,x > 0, and nd-O(r") for all constants d > 0,r > 1.)