請問兩題問題
Ａ. Evaluate
y=2/3 x=2-2y
∫ ∫ (x+2y)e^(y-x) dxdy by making the change
y=0 x=y
of variables u=x+2y v= y-x
ANS:算出x=u-2v/3 y=u+v/3 J=1/3
請問將 x y代換成 u v後 u v的範圍要怎麼算呢？
Ｂ.Use Lagrange multipliers to find the minimal distance
from the origin to the surface z^2 = xy +1
ANS: 長度Ｌ^2 = x^2 +y^2 +z^2
F(x y z)= x^2 +y^2 +z^2-入(xy-z^2 +1)
Fx=2x-入y=0
Fy=2y-入x=0
Fz=2z+2z入=0
請問這樣算是否正確？以及x y z 怎麼算出答案？
謝謝
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