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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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8. Evaluate
where C is the triangle with vertices (0,0),(2,0) and (0,1).
其他申論題
4. Evaluate
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5. Evaluate
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6. Let F = (yz) i + (xz) j + (xy) k, Find div (curl (F)).
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7. Find the minimum value of the function f(x) = 2x3+ 3x2- 36x + 6 on the whole real line.
#530591
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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12. Find the saddle points of the function xy - 2x - y + 7.
#530596
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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