Re: [考古] 台大98研究所考古題

看板trans_math作者Honor1984 (希望願望成真)時間16年前 (2010/01/26 00:21)推噓1(1推 0噓 2→)

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※ 引述《ONIspirit (嘎)》之銘言： : 題目有點多囧... : 勞請板上高手救救我 Q_Q : 2. Given f(x,y) = x^3 + 2xy + y^3 , find the unit vector u such that : the directional derivative of f(x,y) at the point (1,2) and in the direction : → : u attains its maximum. grad f = (3x^2 + 2y)i + (2x + 3y^2)j grad f(1,2) = 5i + 14j u = 1/√[5^2 + 14^2] (5 i + 14 j) : 3. : 8 2 : Evaluate ∫ ∫ sin(y^4) dydx : 0 x^(1/3) 2 y^3 = ∫ ∫ sin(y^4) dx dy 0 0 16 = (1/4)∫sin(y^4)d(y^4) 0 = (1/4) (-cos16 + 1) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.32.251.163

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※ 編輯: Honor1984 來自: 114.32.251.163 (01/26 00:28)

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