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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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高職極限問題lim
Jan 27th 2014, 09:08

首先，你符號好像打錯了，不是n→1，應該是x→1吧？
 
lim(x→1)[a(√x+1)-b]/(x-1)=1 b=?(A)1(b)2(c)3(d)4
  
[Sol]
若將x=1代入原式，分母為0，因此若極限存在，分子也必須為0
即 a(√1+1) -b = 0
2a -b = 0 → b=2a
代入原式
lim(x→1) [a(√x+1) -2a]/(x-1) = 1
lim(x→1) (a√x +a -2a)/(x-1) = 1
lim(x→1) (a√x -a)/(x-1) = 1
lim(x→1) a(√x -1)/(x-1) = 1
分子分母同乘以 √x +1 得
lim(x→1) [a(√x -1)(√x +1)]/[(x-1)(√x +1)] = 1
lim(x→1) [a(x -1)]/[(x-1)(√x +1)] = 1
消去(x-1)
lim(x→1) a/(√x +1) = 1
x=1代入
a/2 = 1
a = 2
因為 b = 2a
所以 b = 4，故選(d) 

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