※ 引述《flygey (努力达成目标)》之铭言： : 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(於两个交点之一以直角相交) : (请问这题方程式如何设) : 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 : (想请问这题界线是设 0-1 还是 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 有错请指正 <(_._)> : 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. : (这题方程式是 f(x,y,z)=x^2+y^2-1+入(x+y+z-1) 这样设吗 : 如果方程式求出xyz後要如何求最近最远点 ) : 请版友指导 : 感谢 --

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