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87年 - 87 中原大學轉學生招生考試(理、工、資電學院聯招):微積分#124719
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12. Find the saddle points of the function xy - 2x - y + 7.
其他申論題
8. Evaluate where C is the triangle with vertices (0,0),(2,0) and (0,1).
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9. Evaluate dzdydx.
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10. Evaluate the integral dydx.
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11. Find the volume of the solid that is bounded above by the sphere ρ=1 and below by the cone ϕ=
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第二部份:計算及證明題 1. Prove that if f is differentiable on (a, b), then f is continuous on (a, b).
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2. Suppose that the function y(x) satisfies the following differential equation: = y(x)(1 - y(x)). If y(0) =, then find y(2). (Hint: separation of variables)
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3. Use Lagrange Multiplier method to calculate the maximum value of x + 2y subject to the condition that ≤ 1.
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4. Evaluate , where R is the region bounded by x + y = 0, x + y = 1, x - y = -1, and x - y = 2.
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一、中譯英(占 8 分 )1. 高中畢業象徵一個階段的結束,同時也是另一個階段的開始。
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2. 我們必須準備好面對新環境所可能帶給我們的挑戰。
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