作者coffee1205 (佐岸)
看板trans_math
标题微积分证明题
时间Sun Oct 19 12:20:03 2008
Let f(x)=x/|x|.Prove that limitf(x) does not exist?
x趋近0
Hint:Show that no number L qualifies as the limit because
there always some x such that |x| < delta,but |f(x)-L|大於等於1/2
,no matter how small delta is taken.
这题我想很久,但是解不出来,有没有哪位好心人士可以帮帮我,小弟感激不尽!!!
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 218.167.170.154
1F：推 zptdaniel:感觉像是成大的考题 123.194.97.168 10/19 14:07
2F：→ Honor1984:直接证明大於等於1不就好了?? 为何1/2?122.124.104.229 10/19 15:08
3F：→ coffee1205:1/2是题目给的,我也不知道为什麽...218.167.170.154 10/19 15:35
4F：推 zptdaniel:你就假设极限存在且其值为L (L为实数) 123.194.97.168 10/19 15:50
5F：→ zptdaniel:利用定义去证明就好. 123.194.97.168 10/19 15:52
6F：推 zptdaniel:hint里面已经给你提示取eplison为 1/2 123.194.97.168 10/19 15:56
7F：→ coffee1205:喔,好,我试试看!!谢谢你罗!!218.167.170.154 10/19 16:01
8F：推 SDUM:ε是 epsilon 218.175.77.43 10/20 08:58
9F：推 zptdaniel:^^" 203.68.127.32 10/20 09:08