### Sequences of Continuous Function, Uniform Convergence and Pointwise Convergence

Let {fn(x)} n-1 ---> infinity be a sequence of continuous functions [0,1] that converges uniformly. a) Show that there exists M>0 such that |fn(x)|<= M (nЄI 0<x<1) b)Does the result in part (a) hold if uniform convergence is replaced by pointwise convergence? ---