作者acgrun (acgrun)
看板trans_math
標題Re: 極限問題？題目有改過
時間Tue Jun 12 00:06:38 2007
*不好意思，題目打錯了，兩題都應該是 ^(1/2)
又有兩題關於極限的問題，我想了半天還是解不出來，
不知是不是因式分解方面的問題，請高手解答一下，謝謝
2-(x+4)^(1/2) 1
1. lim _____________ = - ___
x->0 x 4
2-(x+4)^(1/2)
lim _____________
x->0 x
[2-(x+4)^(1/2)] [2+(x+4)^(1/2)]
= lim __________________________________
x->0 x [2+(x+4)^(1/2)]
2^2 - [(x+4)^(1/2)]^2
= lim _________________________________
x->0 x [2+(x+4)^(1/2)]
4 - (x+4)
= lim _________________________________
x->0 x [2+(x+4)^(1/2)]
- x
= lim _______________________________-
x->0 x [2+(x+4)^(1/2)]
1
= - ___
4
1 1
2. lim ___ ( ___________ - 1 )
x->0 x (1+x)^(1/2)
1 1
lim ___ ( ___________ - 1 )
x->0 x (1+x)^(1/2)
1 1 (1+x)^(1/2)
= lim ___ ( ________________ - _____________ )
x->0 x (1+x)^(1/2) (1+x)^(1/2)
1 1 - (1+x)^(1/2)
= lim ___ ( ___________________________ )
x->0 x (1+x)^(1/2)
1 [1-(1+x)^(1/2)] [1+(1+x)^(1/2)]
= lim ___ ( _______________________________________ )
x->0 x (1+x)^(1/2) [1+(1+x)^(1/2)]
1 1- (1+x)
= lim ___ ( ________________________________________ )
x->0 x (1+x)^(1/2) [1+(1+x)^(1/2)]
1 - x
= lim ___ ( ________________________________________ )
x->0 x (1+x)^(1/2) [1+(1+x)^(1/2)]
- 1
= lim ______________________________
x->0 (1+x)^(1/2) [1+(1+x)^(1/2)]
1
= - ___
2
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◆ From: 218.168.165.104
1F：→ mathmac:第一題題目錯了，應該是根號吧 211.76.80.139 06/12 00:12
2F：→ mathmac:然後第一題把分子有理化之後約分就好了 211.76.80.139 06/12 00:12
3F：→ mathmac:第二題通分完消掉再約分，答案就出來了 211.76.80.139 06/12 00:13
※ 編輯: acgrun 來自: 218.168.156.52 (06/12 04:27)
※ 編輯: acgrun 來自: 218.168.156.52 (06/12 05:29)