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研究所、轉學考(插大)-微積分
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107年 - 107 國立臺灣大學轉學生招生考試試題_(商、管、農、經學院聯招) ：微積分(C)#113212
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其他申論題
8. Find the area of the surface z = xy, x2 + y2 ≦ 1.
#483679
9.y= f(x), y' =2 y(10-y), f(0)=1,f(x)=?
#483680
10. Polar coordinate x = r cosθ , y = r sineθ. Cardioid r = 1 - sinθ . At the point (x,y)=(1,0) d2y/dx2=?
#483681
1.=?
#483682
3. Cardiord x = 2 sin θ - sin 2θ, y = 2 cosθ- cos2θ. Find its total length.
#483684
4. When x = 2 sinθ - sin2θ and y = 2 cosθ - cos2θ,determine d2y/dx2. at θ =π/3.
#483685
5. Consider y = x/(1 + kx) which is a family of hyperbolas. Find its orthogonal trajectories.
#483686
6. When x3 + y3+ z3-3xyz = 1, derive ∂z/∂x and ∂z/∂y.
#483687
7. When f(x,y) = 2xy -+1, find local maxima, local minima, and saddle points.
#483688
8. Find the volume determined by x2+ y2 + z2 ≤1 and x2 + y2 ≤ y.
#483689
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