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96年 - 96 國立臺灣師範大學_學士班轉學生招生考試試題_資訊工程學系二年級：微積分#122363
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題組內容
1. Evaluate the limits in the following problems.
(b)
(15 分)
其他申論題
7. (10分) Find the tangent line to the curve of intersection of the surfaces z = x² + y² and x + y + z = 33 at a point (1, 2, 5).
#521138
8. (10分) Find the maximum value of f(x, y) = 2x + 2xy + ysubject to the constraint 2x + y = 100 by Lagrange multiplier.
#521139
9. (20分) Using Green's Theorem, evaluateclockwise around the boundary curve C of the region R = {(x, y) ∈ R | 1 ≤ y ≤ 2 - x²}, where F = (x² + y²)i + (x² - y²)j. (10分) (請說明 Green's theorem 之公式) (5分) (畫出 R 之圖形)
#521140
(a) (15 分)
#521141
(a) (15 分)
#521143
(b)dx (15 分)
#521144
3. Find the maximum and minimum values of the function shown below and the corresponding values of x on the given interval., x in [-1,1] (20 分)
#521145
4. Find the sum of the following series: (10 分)
#521146
5. Find the equation of the plane that contains the line of intersection of the planes x+y+z=0 and 2x+y-3z=2, and passes through point (2,0,1). (10 分)
#521147
1.Please prove the derivative of Sine function by the limit definition of the derivative. (10 分)[sin x] / dx = cos x
#521148
(15 分) 
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(15 分)