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96年 - 96 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題：微積分#113217
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5. Find the tangent plane of the surface cos πx - x
2
y+ e
xz
+ yz = 4 at the point P
0
(0, 1, 2).
其他申論題
1. If f is a continuous function such that dt for all s, Aad an explicit formula for f(x).
#483725
2. In what direction is the derivative of f(x, y) =at P(1,1) equal to zero?
#483726
3. Find the maximum value of x2 + y2 subject to the constraint x2 - 2x + y2 - 4y = 0.
#483727
4. Suppose that f(0) = -3 and f'(x) ≤5 for all values of x. How large can f(2) possibly be?
#483728
6. Evaluate dA, where R is the parallelogram enclosed by the lines x - 2y = 0, x-2y=4,3x-y=1 and 3x -y = 8.
#483730
7. Find the area of the surface cut from he paraboloid x2 + y2 - z = 0 by the plane z = 2.
#483731
8. Evaluate the integraldy along the circle C : (x-2)2+(y-3)2= 4.
#483732
(a)
#483733
(b)
#483734
(a) Test the series for convergence or divergence.
#483735
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