1.設函數f:(1,+00)->R,f(x)=[(x+1)*x^(1/2)-x/(x-1)^(1/2)]^(1/3)
試求f之導函數
2.試求擺線
x=a(t-sint)
y=a(1-cost)
於0<=t<=2π 間之一節弧之形心(centroid)座標
微積分:導函數、求形心
2014-04-01 8:21 pm
回答 (9)
2014-04-02 3:08 pm
✔ 最佳答案
(2)
c=弧線形心
=弧線中點
=[x(pi),y(pi)]
=(a*pi,2a)......ans
(1)
y=[(x+1)√x-x/√(x-1)]^1/3
y^3=(x+1)√x-x/√(x-1)
√(x-1)*y^3=(x-1)√[x(x-1)]-x
兩邊微分:
√(x-1)*3y^2*y'+y^3/2√(x-1)=√[x(x-1)]+(x+1)(2x-1)/2√[x(x-1)]-1
y'={√[x(x-1)]+(x+1)(2x-1)/2√[x(x-1)]-1-y^3/2√(x-1)}/√(x-1)*3y^2
寫作隱函數比較簡單
2014-05-30 5:03 pm
2014-05-08 4:30 pm
2014-05-02 3:39 pm
2014-05-01 5:33 pm
2014-04-30 10:56 pm
2014-04-28 4:06 pm
2014-04-27 11:02 pm
2014-04-02 9:59 am
收錄日期: 2021-05-02 11:05:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140401000016KK02558