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For n∈Nn\in \mathbb{N}n∈N, let fn:[0,π]→Rf_n:[0, \pi]\to \mathbb{R}fn:[0,π]→R be defined by
fn(x):=sinn(x) f_n(x):= \sin^n (x) fn(x):=sinn(x)
Is the sequence {fn}n=1∞\{f_n\}_{n=1}^{\infty}{fn}n=1∞ uniformly convergent?
Hint: is the limit function continuous?
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