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104年 - 104 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試_A3、A4、A5、A7、951：微積分#112762

科目：研究所、轉學考(插大)-微積分 | 年份：104年 | 選擇題數：0 | 申論題數：11

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (11)

1.Find63ae4582436f2.jpg.Answer:_______

2. If f(x) = Inx + tan-1 x, fnd (f-1)'63ae45ae627f3.jpg, Answer :_________

3. Evaluate 63ae45d4f0e32.jpg. Answer:__________

4. Find the interval of convergence of the power series 63ae45ff7a443.jpg. Answer:__________

5. Find the limit: 63ae46268e8fd.jpgIn t dt. Answer :________
6. Find the maximum rate of change of f(x, y) = x2y+exy sin y at (1,0). Answer :________

7. Find63ae4694cfe95.jpgAnswer : __________

8. Evaluate 63ae46db00fa2.jpgdydc by applying the transformation u =x+y, u = y - 2x and integrating over a appropriate region in the uv-plane. Answer :_____________

1. Sketch the region of integration, reverse the order of integration, and evaluate the integral 63ae4719aeaea.jpgdydx.

2 Find the counterclockwise circulation for the field F'=(x+ ex sin y)it(x+ ex cos y)j along the curve C : The right-hand loop of the lemniscate r2 = cos 2θ.
3. A manufacturer finds that it takes a units of labor and y units of capital to produce f(z,y) = 100x3/4y1/4 units of product. If a unit of labor costs $100, a unit of capital costs $200, and $200,000 is budgeted for production, determine how many units sbould be expended on labor and how many units should be expended on capital in order to maximize production.