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complexnumber
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Homework Statement
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?
Homework Equations
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?