kkk asked in 科學數學 · 1 decade ago

高微convergent uniformly [急]

Let fn(x) = nx/(1+n*x^2),0<=x<=1

(a) Find lim n->+oo fn(x)=f(x=?.

(b) Does fn convergent uniformly to f ?

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上次幫我回答二位 因為時間設太短了 都變成投票 不好意思

所以這次就設長一點 ..

Update:

謝了

1 Answer

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  • 1 decade ago
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    x=0時, fn(x)=0 => fn(x)->0

    x≠0時, fn(x)= x/[1/n + x^2] -> x/x^2= 1/x

    故 fn(x) -> f(x)= { 0 , if x=0

    { 1/x , if x≠0

    f(x)在[0,1]內不是連續函數, 故 fn(x)-> f(x) 不是 uniformly conv.

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