Re: [考古] 幾題計算題請問
※ 引述《flygey (努力達成目標)》之銘言：
: 1.Show that the parabola y=-x^2 and the line x-4y-18=0 intersect at right
: angle at one of their points of intersection(於兩個交點之一以直角相交)
: (請問這題方程式如何設)
: 2.Find the volume of the solid obtained by rotating the region bounded by
: y=x-x^2 and y=0 about the line x=2
: (想請問這題界線是設 0-1 還是 0-2)
y = x - x^2
=> x - x^2 = 0 => (x)(1 - x) = 0 => x = 0 或 1
y = 0
1
V = ∫ (2π)|x-2||y| dx
0
1
= ∫ (2π)(2-x)(x - x^2) dx
0
1
= (2π)(∫ x^3 - (3)(x^2) + 2x dx)
0
x^4 |1
= (2π)(--- - x^3 + x^2 | )
4 |0
1 π
= (2π)(---) = ---
4 2
有錯請指正
<(_._)>
: 3.The plane x+y+z=1 cuts the cylinder x^2+y^2=1 in an ellipse.Use Lagrange
: multipliers to find the points on the ellipse that lie closest to and
: farthest from the origin.
: (這題方程式是 f(x,y,z)=x^2+y^2-1+入(x+y+z-1) 這樣設嗎
: 如果方程式求出xyz後要如何求最近最遠點 )
: 請版友指導
: 感謝
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07/06 10:07, , 1F
07/06 10:07, 1F
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