Re: 極限問題？題目有改過

[acgrun (acgrun)]

*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
→ mathmac:第一題題目錯了，應該是根號吧
→ mathmac:然後第一題把分子有理化之後約分就好了
→ mathmac:第二題通分完消掉再約分，答案就出來了
※ 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)