1. (35 points) Use the definitions to prove that: (a). 2n? + 3n+ 7 = O(n); (b). 100n3- n2 + 5n = O(n) (c). 15n4 + 3n3 = N(n) (d). 2nlog n - 2n2 = 2(12) (e). arnt +ak-in +ao = O(n). Here ar, 4x 1., 21, ao are constants with ak > 0, and k is a positive integer. k1 ++