(a) Let fn: [0, 1] → R be a sequence of continuous functions and fn converges uniformly to a function f : [0, 1] → R. Prove that lim n→∞ [ n(x)}dx = [] 1(a) da n (b) Consider fn : [0, 1] → R defined by fn(2) x² r2 + (1 −nx)2 = x = [0, 1] Show that fn converges uniformly on [8, 1] for all d > 0 but does not converge uniformly on [0, 1]

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