Calculate the big-O estimates for the following functions: (n +n)(n + 1000) (n log? n + n)(n +n?) (2" + :) (3 + 2") (n + n log n)(1+log n) + (n + log n)(n + 1) (2n! + 2") (n! + nn) (n log? n+ n log n)(1+log n + log n+ log n)(1+ log n) (n+ n + n)(2logn + 2log; (1+ + n?)(n + n4 + n) 3 log* n .2 .3 3 2log?. + 2log3 n 3 k=1 E- II(1+ log n)* k=1