tions gn [0, 1] → R given by : Consider the sequence of func- In (x)= = lim gn- (a) Show that (gn) converges uniformly on [0, 1] and find g Show that g is differentiable and compute g'(x) for all r = [0, 1]. (b) Show that (gn) converges pointwise on [0, 1]. Is the convergence uni- form? Let h= lim gn, and compare h and g'. Are they the same? n

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A: This is a question from Maclaurin series.

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A: 12

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A: The solution of given problem is given as follows :

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A: Given function is continuous at x= 0 and x=1. See the attachment.

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A: We can prove it by showing that function is not pointwisw convergent.

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A: The theorem is done .

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