作者LuisSantos ( )
看板trans_math
標題Re: [積分] very難
時間Sat Dec 13 18:24:49 2008
※ 引述《chingyes (axsazxc)》之銘言：
: http://0rz.tw/5b5bZ
: 請問紅線部分
: 如何變過去的
: 請神人指導@@
x - 1 A Bx + C
1. 令 ------------ = --- + ---------
(x)(x^2 + 1) x x^2 + 1
則 x - 1 = (A)(x^2 + 1) + (x)(Bx + C)
= (A + B)(x^2) + Cx + A
A + B = 0 A = -1
C = 1 => B = 1
A = -1 C = 1
x - 1 A B C
2. 令 ------------ = --- + ----- + -------
(x^2)(x + 1) x x^2 x + 1
則 x - 1 = (A)(x)(x + 1) + (B)(x + 1) + (C)(x^2)
= (A + C)(x^2) + (A + B)(x) + B
A + C = 0 A = 2
A + B = 1 => B = -1
B = -1 C = -2
--
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◆ From: 140.119.129.141
1F：推 chingyes:如何知道要分 X 跟 X^2 219.81.152.182 12/13 18:51
2F：→ LuisSantos:這一般的微積分教科書都有寫140.119.129.141 12/13 19:51
3F：推 zptdaniel:分母@@ 118.233.32.58 12/13 19:51
4F：→ zptdaniel:這是劃分項分式 118.233.32.58 12/13 19:51
5F：推 chingyes:啥碗糕@@ 219.81.152.182 12/13 19:57
6F：推 sexysam:回1樓 因為X^2的分子可能為AX+B 140.112.241.48 12/13 21:41
7F：→ sexysam:再拆開就變成X和X^2兩項 140.112.241.48 12/13 21:42