Re: [考古] 96成大
※ 引述《linda1218 (linda)》之銘言：
: 1. show that arctan( x+1 / x-1 )+ arctan(x)=C and find the value C
令a=arctan(x+1/x-1)
b=arctan(x)
tan a=(x+1)/(x-1) <----------我猜x+1/x-1是這意思沒錯吧
tan b=x x+1
------+x
和角 x-1
tan(a+b)=(tana+tanb)/(1-tanatanb)=--------------------------
(x+1)x
1- -------
x-1
x^2+1
=----------=-1 C=arctan(-1)=3π/4+kπ k為整數
-1-x^2
: 2. find the surface area of the portions of the sphere x^2 +y^2 +z^2=4
: that are within the cyclinder (x-1)^2 + y^2 =1
|▽f|
∫∫-----------dA
|▽f˙^p|
|▽f|=√4x^2+4y^2+4z^2=4
|▽f˙^p|=2z
=2∫∫1/z dA
z=√(4-x^2-y^2)
換成極座標
2π 1 d(r^2)dθ
∫ ∫ ----------- rdr=1/2 dr^2(我已經先把外面的2一起消掉了)
0 0 √(4-r^2)
|r=1
=2π*[-√(4-r^2)] | =2π(2-√3)
|0
由於這是假設在z>0的狀況
答案請記得*2
4π(2-√3)
--
聽說現在簽名檔流行放無名是吧
http://www.wretch.cc/album/andyfc1
內無正妹
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.242.85
推
06/16 16:48, , 1F
06/16 16:48, 1F
推
06/16 17:48, , 2F
06/16 17:48, 2F
推
06/17 16:18, , 3F
06/17 16:18, 3F
→
06/17 16:20, , 4F
06/17 16:20, 4F
討論串 (同標題文章)