Re: [分析] 高微 T or F

看板Math作者 (han)時間13年前 (2012/03/24 09:23), 編輯推噓1(1推 0噓 1→)
留言2則, 2人參與, 最新討論串1/1
※ 引述《iddee ()》之銘言： : 對的話證明之，錯則給反例。 : 設 f_n(x): [a,b] -> R 在 [a,b] 上連續且在 (a,b) 上可微 : 若 f_n 均勻收斂至 f : 則 f 在 (a,b) 上可微 This statement is not ture. The counterexample can be constructed as following: we know there exists an function defined on [a,b] which is continuous on [a,b] but is not differentiable on (a,b). On the other hand, any continuous function on a closed and bounded interval can be uniformly approximated by the polynomials ( Weierstrass approximation theorem). Hence, the counterexample exists. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.104.65
推
03/24 11:19, , 1F
第四行 第二個[a,b]應該要改成 (a,b)會較好吧
03/24 11:19, 1F
※ 編輯: zhanguihan 來自: 140.112.104.65 (03/24 11:26)
→
03/24 15:07, , 2F
as follow
03/24 15:07, 2F
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文章代碼(AID): #1FRI8U-P (Math)