推 dearcherry11:謝謝:) 02/06 16:47
※ 引述《dearcherry11 (小笨寶)》之銘言：
: Let fn(x)=x^n/1+x^n for x in the interval [0,2]. Prove that the sequnece {fn}
: of functions converges pointwise on [0,2] but the convergence of {fn} is not
: uniformly on [0,2]
: 拜託大大囉^^"
1 1<x<=2
(1) Consider f(x) = 0.5 x=1
0 0<=x<1
It's easy to show that fn(x) -> f(x) pointwise in [0,2]
(2) However, since f(x) is not continuous, so the convergence is not uniform
Reason: If fn are continuous and unifrom converge, then f(x) is continuous
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