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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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8. Let f(x,y) = x
4
+y
4
-4xy + 1. Find local maxima, local minima, and saddle points of f(x, y).
其他申論題
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
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
3. Convert the integral dzdydx to an equivalent integral in cylindrical coordinates. Answer :__________(Do not evaluate the integral).
#483660
4. Evaluate the integral Answer : ____________
#483661
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