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ANA2 · 1

Uniform convergence

11 concepts · 28 questions

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ANA2Step●○○○○new1 Uniform convergence
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The problem

Let fn(x)=nx1+n2x2f_n(x) = \frac{n x}{1 + n^2x^2} on [0,1][0, 1]. (a) Find the pointwise limit. (b) Is the convergence uniform on [0,1][0, 1]? On [δ,1][\delta, 1] for δ>0\delta > 0? (c) Does ∫01fn→0\int_0^1f_n\to0?

Find the pointwise limit.