[微積] 解釋

看板Math作者 (李孟李孟)時間15年前 (2011/01/24 22:59), 編輯推噓2(2推 0噓 10→)
留言12則, 2人參與, 最新討論串1/1
Let — x if x is rational f(x)∣ —-x if x is irrational Find each valu,if possble. (a) lim f(x) x→1 答案是：no exist 請問要如何解釋？ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.0.235.49
推
01/24 23:04, , 1F
找兩個seq.一個從有理數靠近1 一個從無理數靠近1
01/24 23:04, 1F
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01/24 23:04, , 2F
(比如說用1+1/n當作有理數)(然後Q是dense在|R所以可
01/24 23:04, 2F
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01/24 23:04, , 3F
找到) 這樣應該可以吧
01/24 23:04, 3F
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01/24 23:15, , 4F
那下面這題為什麼找得到？
01/24 23:15, 4F
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01/24 23:15, , 5F
f(x)= x^2 if x is rational
01/24 23:15, 5F
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01/24 23:15, , 6F
f(x)= x^4 if x is irrational
01/24 23:15, 6F
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01/24 23:16, , 7F
For what values of a does lim f(x) exist?
01/24 23:16, 7F
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01/24 23:16, , 8F
x→a
01/24 23:16, 8F
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01/24 23:17, , 9F
答案是： a = -1、0、1
01/24 23:17, 9F
推
01/24 23:34, , 10F
如果極限存在 則從有理數逼近和從無理數逼近要一樣
01/24 23:34, 10F
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01/24 23:35, , 11F
所以a^2=a^4 =>a^2(a^2-1)=0 => a=-1 0 1
01/24 23:35, 11F
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01/25 00:03, , 12F
了解了！謝謝你！
01/25 00:03, 12F
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