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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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3. Trochoid x = 20 - sinθ, y = 2 - cosθ. Find the tangent line of the curve at θ =
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其他申論題
8. (10 points) Evaluate ∫∫R xy dA , where R is the region bounded by and y=0, by converting to Polar Coordinates.
#483646
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.
#483647
1.=?
#483648
2. Find f'(2) if f(x)= and g(x) =
#483649
4. Trochoid x = 2θ - sinθ, y = 2 - cos θ. Find the area under the curve and above the x-axis for 0≤θ≤2π.
#483651
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.
#483652
6. Let the region R be enclosed by the curves y = x2 and y = 2 - x2. Find the arc length of the region R.
#483653
7. Evaluate where R is the trapezoidal region with vertices (1,0), (2,0), (0,2) and (0,1).
#483654
8. Let f(x,y) = x4+y4-4xy + 1. Find local maxima, local minima, and saddle points of f(x, y).
#483655
9. Find the absolute maximum value and absolute minimum value of f(x,y) =x4+y4 -4xy + 1 on the disk x2+y2≤1.
#483656
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