Question: Consider fn(x) = nx (1 -x) for x E [0, 1]. (a) Find f(x) = lim fr(x). (b) Does fn -> f uniformly on [0,

Consider fn(x) = nx" (1 -x) for x E [0, 1].

Consider fn(x) = nx" (1 -x) for x E [0, 1]. (a) Find f(x) = lim fr(x). (b) Does fn -> f uniformly on [0, 1]? Justify. (c) Does for fn(x) dx converge to f f(x) dx? Justify

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