Let (fn)n≥1 be the sequence of functions defined on [0, 1] by
\(f_n(x)=x^n \log \left(\frac{1+\sqrt{x}}{2}\right) .\)
Which of the following statements are true?
1
(fn) converges pointwise on [0, 1].
2
(fn) converges uniformly on compact subsets of [0,1) but not on [0,1).
3
(fn) converges uniformly on [0,1) but not on [0,1].
4
(fn) converges uniformly on [0, 1].