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研究所、轉學考(插大)-微積分
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112年 - 112 臺灣聯合大學系統(清華、陽交、中央 聯招)學士班轉學生考試_A3、A4、A6理工組：微積分#117689
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8. Eraluate the integal
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4.Consider the region bounded by the graphs of y = In x, y = 0, and x = e. Find the volume of the solid formed by revolving the region about the x-axis.
#502899
5. Find the derivative of f(x,y,x) = xyz in the direction of the velocity vector of the helix r(t) = (cos3t)i + (sin 3t)j + 3tk at t = π/3.
#502900
6. Evaluate the integraldydx.
#502901
7. Evaluate the integral dA, where R is the region inside the upper semicircle of radius 2 centered at the origin, but outside the circle x2 + (y - 1)2 = 1.
#502902
(a) (6 分) Determine whether the series converges absolutely or converges conditionally or diverges and give reasons for your answer.
#502904
(b) (6 分) Find all values of x for whichconverges and give reasons for your answer.
#502905
(a) (4 分) Show that f is not continuous at (0, 0).
#502906
(b) (4 分) Find the partial derivative at (2,y) if x3 +y3≠0.
#502907
(c) (4分) Use the definition of the partial derivative to find af at (x, y) = (0,0).
#502908
3. Find the absolute maximum and minimum values of f(x,y) = x2 + 3y2 + 2y on the unit disk x2 + y2 ≤1.
#502909
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