作者coffee1205 (佐岸)
看板trans_math
標題微積分證明題
時間Sun Oct 19 12:20:03 2008
Let f(x)=x/|x|.Prove that limitf(x) does not exist?
x趨近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.
這題我想很久,但是解不出來,有沒有哪位好心人士可以幫幫我,小弟感激不盡!!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.167.170.154
1F：推 zptdaniel:感覺像是成大的考題 123.194.97.168 10/19 14:07
2F：→ Honor1984:直接證明大於等於1不就好了?? 為何1/2?122.124.104.229 10/19 15:08
3F：→ coffee1205:1/2是題目給的,我也不知道為什麼...218.167.170.154 10/19 15:35
4F：推 zptdaniel:你就假設極限存在且其值為L (L為實數) 123.194.97.168 10/19 15:50
5F：→ zptdaniel:利用定義去證明就好. 123.194.97.168 10/19 15:52
6F：推 zptdaniel:hint裡面已經給你提示取eplison為 1/2 123.194.97.168 10/19 15:56
7F：→ coffee1205:喔,好,我試試看!!謝謝你囉!!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