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研究所、轉學考(插大)-微積分
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109年 - 109 台灣綜合大學系統_學士班轉學考聯合招生考試：微積分C#124121
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8. (10 points) Find the absolute maximum of f(x, y) = e
-xy
on the region x² + 4y² ≤ 1.
其他申論題
4. (10 points) Find the arc length of the polar curver =θwith 0 ≤ 0 ≤ π.
#527612
5. (10 points) Find the volume of the solid of revolution about the x-axis bounded by the curvef(x) =with x ∈ [1,0∞).
#527613
6. (10 points) Consider the power series Find its maximal domain of convergence.
#527614
7. (10 points) Recall that the hyperbolic tangent function tanh x=,x∈Ris one to one and has the inverse function f(x) = tanh-1x. Find the Maclaurin series off(x) = tanh-1x.
#527615
9. (10 points) Evaluate the line integraly3dx – x³dy, where C is the circle x² + y² = 8 with positive orientation.
#527617
10. (10 points) Let F(x, y, z) = xi + yj – 2zk. Suppose that the closed surface S is defined by the paraboloid y = x² + z² with 0 ≤ y ≤ 1. Find the flux of F outward across S.
#527618
(一) 假設兩流體為逆流，總熱傳係數(Overall Heat Transfer Coefficient) U = 350 W/m2∙K，試計算水的出口溫度。(5 分)
#527619
(二) 兩流體為逆流狀態，試計算熱傳面積。(5 分)
#527620
(三) 若兩流體為順流狀態，試計算熱傳面積。(10 分)
#527621
(一) 在操作精餾塔時，若提高塔頂回流比，其產生之優缺點為何？(6 分)
#527622
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