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  3. 1 consider the sequence of functions fn 0 j...

Question: 1 consider the sequence of functions fn 0 j...

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1. Consider the sequence of functions fn : [0, j → R defined by nax 1 + a) Does the sequence of numbers 0o n (x) dx 0 have a limit? Explain how you know that fn is integrable on [0, 1 (b) Is it possible that fn converges uniformly to some function f 0,R? Explain which theorem from the lecture informs your anwer. (c) For each x e 10, 1], give the limit of fn (x). (Hint: Consider separately x = 0 and x 〉 0.

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