1. (35 points) Use the definitions to prove that: (a). 2n2 + 3n + 7 = O(n2); (b). 100n3 12 + 5n = O(n) . (c). 15n" + 3n3 = N(n) (d). 2nlog n - 2n2 = S2(n) (e). axnk + ak-ink-1 + ... + ao = O(n). Here ak, ak-1,..., 21, ao are constants with ak > 0, and k is a positive integer