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研究所、轉學考(插大)-微積分
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109年 - 109 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)#113209
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其他申論題
6. (10 points) Determine and classify the stationary points of the function f(x,y)=xy+(x-y)3.
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7. (10 points) Evaluate
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8. (10 points) Evaluate ∫∫R xy dA , where R is the region bounded by and y=0, by converting to Polar Coordinates.
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9. (10 points) A certain gas satisfies the law where p=presure, V=volume, and T=temperature. Calculate and at the point where p=V=1 and T=2.
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2. Find f'(2) if f(x)= and g(x) =
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3. Trochoid x = 20 - sinθ, y = 2 - cosθ. Find the tangent line of the curve at θ = .
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4. Trochoid x = 2θ - sinθ, y = 2 - cos θ. Find the area under the curve and above the x-axis for 0≤θ≤2π.
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5. Let the region R be enclosed by the curves y = x2 and y = 2 -x2. Find the volume of the solid obtained by rotating the region R about x=1.
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6. Let the region R be enclosed by the curves y = x2 and y = 2 - x2. Find the arc length of the region R.
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7. Evaluate where R is the trapezoidal region with vertices (1,0), (2,0), (0,2) and (0,1).
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