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研究所、轉學考(插大)-微積分
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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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題組內容
2. Find the derivatives of the following functions.
(b) (5 分) f(x) =
+ 5sin x
其他申論題
5. Find the equation of a plane that is perpendicular to the plane 2x-3y+z=3 and passes through (-1,1,-1) and (2,2,1). (10 分)
#521115
6. Find the maxima and minima of the function f(x, y) = x² + 3xy + y² subject to the constraint x² + y² ≤ 1. (20 分)
#521116
1. (10 分) Show that the following limit does not exist.
#521117
(a) (5 分) f(x) =cos x
#521118
(c) (5 分) f(x) =
#521120
(a) (5 分)∫x2 ex3dx
#521121
(b) (10 分)dx
#521122
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
+ 5sin x
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+ 5sin x