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97年 - 97 國立臺灣師範大學_轉學生招生考試試題_資訊工程學系二年級：微積分#122360
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題組內容
1. Evaluate the following integrals.
(b)
(15 分)
其他申論題
4. (15%) A solid ball can be obtained by revolving the semi-circular region x² + y² ≤ R², x ≥ 0, about the y-axis. Use the method of disks or cylindrical shells to find the volume of such a solid ball.
#521107
5. (15%) Let M, N, k be three positive constants, with M> N. Solve the differential equation = k(M - y)(N - y),under the initial condition y(0) = 0.
#521108
6. (15%) Suppose x units of labor and y units of capital are required to producef(x, y) = 100x3/4y1/4units of a certain product. If each unit of labor costs $200 and each unit of capital costs $300 and a total of $60,000 is available for production, determine how many units of labor and how many units of capital should be used to maximize production.
#521109
(a) (15 分)
#521110
2. Evaluate the limit of the following expression. (15 分)
#521112
3. Find the sum of the following series. (15 分)
#521113
4. Find the 3th Taylor polynomial (centered at 1) of the function f(x) = ln(x+1). (10 分)
#521114
5. Find the equation of a plane that is perpendicular to the plane 2x-3y+z=3 and passes through (-1,1,-1) and (2,2,1). (10 分)
#521115
6. Find the maxima and minima of the function f(x, y) = x² + 3xy + y² subject to the constraint x² + y² ≤ 1. (20 分)
#521116
1. (10 分) Show that the following limit does not exist.
#521117
(15 分)
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(15 分)