Re: 台大數假ㄧ題證明

看板trans_math作者pobm時間18年前 (2007/06/16 12:22)推噓10(10推 0噓 19→)

留言29則, 4人參與討論串1/1

※ 引述《HUJIKOLP (UUOJKLJLKJK)》之銘言： : Let f be continuous on a rectangular region (a,b)X(c,d) : prove that the function F defined by : F(X)=Sf(x,y)dy 積c~d x屬於(a,b)is continuous on(a,b) 有錯請指正囉~~ d F(x)=∫ f(x,y)dy c d F(x+h)=∫ f(x+h,y)dy c d d lim F(x+h)-F(x) = lim [(∫ f(x+h,y)dy) -(∫ f(x,y)dy)] h→0 h→0 c c d =lim ∫[f(x+h,y)-f(x,y)]dy fix x, and let f(x+h,y)-f(x,y)=G(y) h→0 c d =lim ∫ G(y)dy h→0 c (let P={c=a1,a2,....an=d} is a partition of [c,d] Max|P|→0 as n→∞) 1 =lim lim --- ΣG(ai) h→0 n→0 n 1 =lim --- Σ lim G(ai) n→0 n h→0 d = ∫ {lim [f(x+h,y)-f(x,y)]} dy c h→0 ----------------------- 這項因為f在(a,b)X(c,d)連續故為0 =0 lim F(x+h) = F(x) h→0 : ＝≒≠≡≡＜＞≦≧ : ∴∵∫∮∩∪㏑㏒√→∞∠△° : ⅠⅡⅢⅣⅤⅥⅦⅧⅨⅩ : ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ : αβγδεζηθικλμνξοπρστυφχψω -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 125.226.173.220 ※ 編輯: pobm 來自: 125.226.173.220 (06/16 12:22)

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HUJIKOLP

06/16 12:28, , 1^F

06/16 12:28, 1^F

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