Urgent! Please answer all parts with justification, thank you.

Question 4 Part (a). Let fn (x) = cos (nti)x n , for x ER and n EN . (i) Calculate f(x) = limn co fn (x) and determine the domain of f(a) (ii) Show that (fn (x) ) uniformly converges to f(x) on [-1, 1] . (iii) Is (fn (a)) uniformly converging to f(x) on R ? Part (b). The sequence (an ) is given by: al > 0 , anti = 2n 2ntan , for n EN . (i) Prove that (an ) is convergent and find its limit. (ii) Find the radius of convergence R of the power series _(1 - an) zn . (iii) At z = R , determine if the power series is divergent, conditionally convergent, or absolutely convergent