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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_地球科學系二年級：微積分#122361
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8. (10 分) Find the maximum value of f(x, y) = 2x + 2xy + y subject to the constraint 2x + y = 100 by Lagrange multiplier.
其他申論題
4. (10 分) g(x) =f(t)dt, where $f$ is a function whose graph is shown as Fig. 1. Calculate g(6) and g'(6).
#521123
5. (5 分) Use the Integral test to determine the convergence or divergence of the following series.
#521124
6. (5 分) Use the Ratio or Root Test to determine the convergence or divergence of the following series.
#521125
7. (10 分) Find the tangent line to the curve of intersection of the surfaces z = x2 + y2andx + y + z = 33 at a point (1, 2, 5).
#521126
9. (20 分) Using Green's Theorem, evaluate clockwise 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 (5 分))
#521128
1. (10分) Show that the following limit does not exist.
#521129
(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
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