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研究所、轉學考(插大)-微積分
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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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1. If f is a continuous function such that
dt for all s, Aad an explicit formula for f(x).
其他申論題
7. Findat the point (x,y,z)= (2,-1,1) if w=x2+y2+z2 and z3-xy+yz+y3=1 (10%)
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8. Two sides of a triangle are 10cm and 15cm, and are increasing at 3cm/sec and 4cm/sec, respectively, which the included angle is π/3 and decreasing at 0.5 rad/sec. Is the third side increasing or decreasing? at what rate? (12%)
#483722
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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
5. Find the tangent plane of the surface cos πx - x2y+ exz + yz = 4 at the point P0(0, 1, 2).
#483729
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
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#483731
dt for all s, Aad an explicit formula for f(x).
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dt for all s, Aad an explicit formula for f(x).