Let M> 0 be a positive integer and an > 0. (a) Prove rigorously that if lim n = CM for c> 0, then n-x (b) Prove rigorously that lim Tn = c. C. n-x nM+cos M n lim n nM COSM n lim 818 (c) Using the estimates from (a) and (b), prove rigorously that nM+cos. n COSM n nM = 1. - M = 1.