作者LuisSantos (^______^)
看板trans_math
标题Re: [考古] 87二技
时间Wed May 23 16:30:26 2007
※ 引述《kusorz (^~^)》之铭言：
: 1-cosx + tanx-sinx
: lim (______ _______ )
: x→0 x^2 x^3
1 - cosx tanx - sinx
lim (---------- + -------------)
x→0 x^2 x^3
(x)(1 - cosx) + (tanx - sinx)
= lim -------------------------------
x→0 x^3
x - (x)(cosx) + tanx - sinx
= lim -----------------------------
x→0 x^3
1 - cosx + (x)(sinx) + (secx)^2 - cosx
= lim ----------------------------------------
x→0 (3)(x^2)
1 - 2cosx + (x)(sinx) + (secx)^2
= lim ----------------------------------
x→0 (3)(x^2)
2sinx + sinx + (x)(cosx) + (2)(secx)(secx)(tanx)
= lim --------------------------------------------------
x→0 6x
3sinx + (x)(cosx) + (2)((secx)^2)(tanx)
= lim -----------------------------------------
x→0 6x
3sinx (x)(cosx) (2)((secx)^2)(tanx)
= lim ----- + lim --------- + lim ---------------------
x→0 6x x→0 6x x→0 6x
sinx cosx 1 tanx
= lim ------ + lim ------ + lim ((secx)^2)(---)(----)
x→0 2x x→0 6 x→0 3 x
1 sinx 1 1 tanx
= (---)(lim ----) + --- + (---)(lim ((secx)^2))(lim ----)
2 x→0 x 6 3 x→0 x→0 x
1 1 1
= (---)(1) + --- + (---)(1)(1)
2 6 3
1 1 1
= --- + --- + ---
2 6 3
3 + 1 + 2 6
= ----------- = --- = 1
6 6
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.119.66.22
1F：推 kanx:L兄 这一题考不考虑用级数解来作? 220.133.130.61 05/23 17:24
2F：推 lukechen90:还是算的出来阿= =,只是慢了点XD 219.68.232.104 05/23 22:42
3F：推 lukechen90:不过我佩服此PO的勇气,做好久= = 219.68.232.104 05/23 22:53