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# 求解一題向量微積分題目(20點)

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寫在紙上 之後拍照貼上來就可以 謝謝

### 2 Answers

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- 麻辣Lv 77 years agoFavorite Answer
(2a) f(x,y,z)=x^2*y^3-4y+x*z^2▽f(x,y,z)=[2xy^3+z^2;3x^2*y^2-4;2xz]

(2b) Duf(x,y,z)=▽f(x,y,z)*u; u=<2,3,1>▽f(2,3,4)=(2xy^3+z^2;3x^2*y^2-4;2xz)=(2*2*27+16;3*4*9-4;2*2*4)=(124;104;16)=(31,26,4)▽f(2,3,4)*u=(31,26,4)*(2,3,1)=(62+78+4)=144=Projection on uans=144*u/|u|=(2,3,1)*144/√14

(2c) Normal=▽f(x,y,z)=▽f(2,3,4)=(31,26,4)Plane => 31(x-2)+26(y-3)+4(z-4)=0........ans

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