(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For [tex]k = 1,2,\ldots[/tex] define [tex]f_k : \mathbb{R} \to \mathbb{R}[/tex]

by [tex]f_k(x) = \sqrt{k} x^k (1 - x)[/tex]. Does [tex]\{ f_k \}[/tex] converge? In

what sense? Is the limit integrable? Differentiable?

2. Relevant equations

3. The attempt at a solution

I don't know how to approach this question. How can I determine if the sequence converges? What are the theorems to dertermine if the limit is differentiable or integrable?

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# Homework Help: Convergence, differentiable, integrable, sequence of functions

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