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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.
(a)
(15 分)
其他申論題
6. (5分) Use the Ratio or Root Test to determine the convergence or divergence of the following series.
#521137
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
(b) (15 分)
#521142
(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
(15 分) 
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(15 分)