一題極限的證明

看板trans_math作者 (小貝)時間17年前 (2008/11/13 21:49), 編輯推噓0(0推 0噓 6→)
留言6則, 2人參與, 最新討論串1/1
定義:f(x)=x,x rational 0,x irrational (a)Show that f is not diff on 0. g(x)=x平,x rational 0 ,x irrational (b)Show that g is diff at 0 and give g'(0) 據說正確解法要用delta,epsilon法 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.114.216.112
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11/13 22:58, , 1F
(a)f'(x屬於Q) =1≠f'(x不屬於Q)=0
11/13 22:58, 1F
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11/13 22:59, , 2F
(b)f'(x屬於Q)=f'(x不屬於Q)=>2x=0, 只有在
11/13 22:59, 2F
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11/13 22:59, , 3F
x=0處可微分。
11/13 22:59, 3F
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11/14 10:21, , 4F
樓上寫法很可能得 0 分!
11/14 10:21, 4F
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11/14 10:22, , 5F
也不見得需用到ε-δ的討論;
11/14 10:22, 5F
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11/14 10:23, , 6F
用 "可微" 或 "導數" 的定義即可.
11/14 10:23, 6F
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文章代碼(AID): #19731Vy5 (trans_math)