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研究所、轉學考(插大)-微積分
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106年 - 106 國立臺灣師範大學_轉學生招生考試試題_資訊工程學系二年級：微積分#120316
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題組內容
4.
(c) (6 分) Evaluate
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其他申論題
(b) (10 分) Solve the differential equation .
#512522
(c) (10 分) Solve the differential equation 2y' = eˣ/² + y.
#512523
(a) (6 分) Find the limit of the sequence {aₙ}, where aₙ = .
#512524
(b) (8 分) Find the radius and interval of convergence of the series .
#512525
(a) (8 分) Find the value of at the point (1, 1, 1) if the equationxy + z³x - 2yz = 0defines z as a function of the two independent variables x and y and the partial derivative exists.
#512527
(b) (10 分) Find the derivative of f(x,y,z) = x³ - xy² - z at point P₀ (1,1,0) in the direction of the vector v = 2i - 3j + 6k.
#512528
7. (12 分) The usual way to evaluate the improper integraldx (from 0 to ∞) is first to calculate its square: dxdy (double integral from 0 to ∞ for both x and y). Evaluate the integral and solve the resulting equation for I.
#512529
一、王老師發現小明沒有和同學一起去上體育課，反而在教室裡偷取同學的財物。王老師該如何輔導小明？試舉出三項說明之。
#512530
(1)分別於「前備階段」(forethought phase)跟「表現階段」(performance phase)各舉出一個小孟在準備考試時出現的問題。
#512531
(2)針對小孟的兩個問題，分別提出教 師可以協助小孟改善的一個對應策略。
#512532
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