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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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10. Evaluate the integral
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其他申論題
6. Let F = (yz) i + (xz) j + (xy) k, Find div (curl (F)).
#530143
7. Find the minimum value of the function f(x) = 2x³ + 3x² - 36x + 6 on the whole real line.
#530144
8. Evaluate where C is the triangle with vertices (0,0),(2,0) and (0,1).
#530145
9. Evaluate dzdydx.
#530146
11. Find the volume of the solid that is bounded above by the sphere ρ=1 and below by the cone ϕ=
#530148
12. Find the saddle points of the function xy - 2x - y + 7.
#530149
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).
#530150
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)
#530151
3. Use Lagrange Multiplier method to calculate the maximum value of x + 2y subject to the condition that ≤ 1.
#530152
4. Evaluate , where R is the region bounded by x + y = 0, x + y = 1, x - y = -1, and x - y = 2.
#530153
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