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研究所、轉學考(插大)-微積分
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112年 - 112 臺灣聯合大學系統(清華、陽交、中央 聯招)學士班轉學生考試_A3、A4、A6理工組：微積分#117689
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4.Consider the region bounded by the graphs of y = In x, y = 0, and x = e. Find the volume of the solid formed by revolving the region about the x-axis.
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3. Suppose a units of labor and y units of capital are required to produce units of a certain product. If each unit of labor costs $200, each unit of capi- tal costs $300, and a total of $60,000 is available for production, determine how many units of Iabor and how many units of capital should be used to maximize production.
#502895
1. Find the limit
#502896
2. Find f'(-1) if f(x)=e g(x) and g(x)=tan-1(x2)+dt.
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3. Find the length of the curve x = In(sect + tant) - sint, y = cost, 0≤t≤π/3.
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5. Find the derivative of f(x,y,x) = xyz in the direction of the velocity vector of the helix r(t) = (cos3t)i + (sin 3t)j + 3tk at t = π/3.
#502900
6. Evaluate the integraldydx.
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7. Evaluate the integral dA, where R is the region inside the upper semicircle of radius 2 centered at the origin, but outside the circle x2 + (y - 1)2 = 1.
#502902
8. Eraluate the integal
#502903
(a) (6 分) Determine whether the series converges absolutely or converges conditionally or diverges and give reasons for your answer.
#502904
(b) (6 分) Find all values of x for whichconverges and give reasons for your answer.
#502905
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