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研究所、轉學考(插大)-微積分
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106年 - 106 國立暨南國際大學_轉學生入學考試試題_應化系二、土木系二、應光系二：微積分#124594
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題組內容
5. (20%) Polar equation r = 4 cos 3θ
(b) (8%) Find the tangents at the pole.
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3. (10%) Find the average value of f(x) = sin²x on the interval [0, 2π]
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(a) (10%) Find the Maclaure series for f(x) = ln(1+x) and the interval of convergence.
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(b) (5%) Evaluate
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(a) (5%) Sketch the curve.
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(c) (7%) Find the area enclosed by the curve.
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(a) (10%) Find the center of mass.
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(b) (10%). Find the moment inertia about the z-axis.
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7. (10%) Find the area of the surface give by the hemisphere z = f(x, y) = over the region R: x² + y² ≤ 4
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1. A right triangle is formed by the coordinate axes and a line through the point (2, 5). Express the area of the triangle as a function of the x-intercept and calculate the minimal area of the triangle. (20%)
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(a) ∫e2ˣ sin 2x dx (10%)
#529926
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