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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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6. Let the region R be enclosed by the curves y = x
2
and y = 2 - x
2
. Find the arc length of the region R.
其他申論題
2. Find f'(2) if f(x)= and g(x) =
#483649
3. Trochoid x = 20 - sinθ, y = 2 - cosθ. Find the tangent line of the curve at θ = .
#483650
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
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
10. Solve the differential equation xy' = y + x2 sin x with y(π) = 2π.
#483657
1. If f'(0) =-1, find.Answer : ________
#483658
2. Find dt. Answer:_________
#483659
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