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研究所、轉學考(插大)-微積分
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87年 - 87 中原大學轉學生招生考試_理、工學院_應用數學系：微積分#124620
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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).
其他申論題
9. Evaluate dzdydx.
#530146
10. Evaluate the integral .
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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.
#530149
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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(a) y = (x²-1)(x²+x+1)
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(b) y = cos(sin 2x)
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(c) y= sin⁻¹(sec x),
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