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研究所、轉學考(插大)-微積分
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81年 - 81 中原大學轉學生招生考試_應用數學系：微積分#124621
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題組內容
1. Find the following derivatives dy/dx.
(a) y = (x²-1)(x²+x+1)
其他申論題
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
(b) y = cos(sin 2x)
#530155
(c) y= sin⁻¹(sec x),
#530156
(a) ∫xsinxdx
#530157
(b)
#530158
(c)
#530159
(a)
#530160
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