[微積] 一些問題
sin(πx)
1.If f(x)=exp(g(x)), where g(x)=∫ √(1+t^2)dt. find f'(1)
0
2.The base of a solid is the ellipse x^2+4y^2=4, and every parallel cross
sections perpendicular to the x-axis are equilateral triangles. Find the
volume of the solid?
3.Let S be the surface of the solid E that lies above the cone z=√(x^2+y^2)
and below the sphere x^2+y^2+z^2=z and F(x,y,z)=(z,y,sin(x+y)). Evaluate
∫∫ F‧dS =?
S
4.Use the formula x^x=e^(xlnx) and the Maclaurin series for e^x to derive
the formula 1 x ∞ n-1 n
∫ x dx= Σ((-1) )/(n )
0 0
5.Let f(x,y)=8xy-2x-4y+5. Find the absolute minimum value of the function
f(x,y) in the set D, where D is the region bounded by the parabola y=x^2
and the line y=4.
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※ 編輯: stman 來自: 210.66.246.68 (02/07 08:04)
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