極限問題？(題目錯了，已更正)(已解答)
*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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※ 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)