1. (35 points) Use the definitions to prove that: (a). 2n2 + 3n+ 7 = O(n2); (b). 100n3 na +5n = O(n) (c). 15n4 + 3n3 = N(n4) (d). 2n logn 2n2 = 12(na) (e). aknk + ak-ink- + ... + ao = O(nk). Here ak, Ak-1, ak > 0, and k is a positive integer. k-1 , 21, are constants with