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In: Advanced Math

Find the pointwise limit f(x) of the sequence of functions fn(x) = x^n/(n+x^n) on [0, ∞)....

Find the pointwise limit f(x) of the sequence of functions fn(x) = x^n/(n+x^n) on [0, ∞). Explain why this sequence does not converge to f uniformly on [0,∞). Given a > 1, show that this sequence converges uniformly on the intervals [0, 1] and [a,∞) for any a > 1.

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Colby Messinger answered 1 year ago
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