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97年 - 97 國立臺灣師範大學_學士班轉學生招生考試試題_物理系二年級：微積分#122362
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題組內容
3. Evaluate each integral.
(b) (10分)
dx
其他申論題
(a) (5分) f(x) = x² +cos x
#521130
(b) (5分) f(x) = 7 + 5sin x
#521131
(c) (5分) f
#521132
(a) (5分) ∫ x²ex3 dx
#521133
4. (10分) Let g(x) =f(t)dt, where f is a function whose graph is shown as Fig. 1. Calculate g(6) and g'(6).
#521135
5. (5分) Use the Integral test to determine the convergence or divergence of the following series.
#521136
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
dx
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dx