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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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4. When x = 2 sinθ - sin2θ and y = 2 cosθ - cos2θ,determine d
2
y/dx
2
. at θ =π/3.
其他申論題
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
2.=?
#483683
3. Cardiord x = 2 sin θ - sin 2θ, y = 2 cosθ- cos2θ. Find its total length.
#483684
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
9. When x2 + y2 =z2 and x + 2z = 4, determine the maximum value of z.
#483690
10.Ω=｛(x,y)|x≥0,y≥0,x+y≥3｝. Find dxdy.
#483691
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