20) Let I be an interval and let fn : I -> R for each n E N. We say that the sequence { fr } of functions converges pointwise to f : I - R on / if lim fn(x) = f(x) n-+00 for every x E I. Which of the following statements are true? a) If fn(x) = sin(") for each n E N, then {fr} converges pointwise to the function f (x) = 0 on [0, 1]. b) If fn() = x" for each n E N, then {fr} converges pointwise to a function f on [0, 1]. c) If each f, is a continuous function and { fn } converges pointwise to f on [0, 1], then f is also continuous on [0, 1]. d) Assume that f is differentiable on R. Let gn(x) = fetal 2. Then {9n} converges pointwise on R to f