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97年 - 97 國立暨南國際大學_轉學生入學考試試題_應化系二：微積分#124595
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題組內容
2. Evaluate the following integrals:
(a) ∫e
2ˣ
sin 2x dx (10%)
其他申論題
(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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(b)dx (10%)
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(c)(10%)
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(d)dy dx (10%)
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(a) From the Newton's second law, F=ma, solve the differential equation to find v = v(t). (10%)
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(b) What happens to v(t) as t→∞. (10%)
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4. Show that the f function (f(x, y, z) =) satisfies Laplace's equation in three dimensions. (20%)
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