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※ 編輯: Honor1984 來自: 114.32.251.163 (01/26 00:28)
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推 ONIspirit:非常感謝!! 59.104.235.156 01/26 01:14
※ 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)
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