[Solved] Calculate the potential function g for the vector field F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2 z+3 z^2] with g(0,0,0)=0. Then g(x, y, z)=
Question: Calculate the potential function \(g\) for the vector field \(F(x, y, z)=\left[\begin{array}{c}y e^{2 z} \\ x e^{2 z} \\ 2 x y e^{2 z}+3 z^{2}\end{array}\right]\) with \(g(0,0,0)=0\). Then \(g(x, y, z)=\) ?
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(Solved) Calculate the area of the region bounded by the simple
(Steps Shown) Suppose (partial N)/(∂ x)-(partial M)/(∂
![[Steps Shown] Calculate vecF • d r](/images/solutions/MC-solution-library-46347.jpg "[Steps Shown] Calculate vecF • d r with the field F from problem")
[Steps Shown] Calculate vecF • d r with the field F from problem
![[All Steps] Calculate \oint F • n#770;](/images/solutions/MC-solution-library-46348.jpg "[All Steps] Calculate \oint F • n#770; d s with the field")
[All Steps] Calculate \oint F • n#770; d s with the field
Solution: Find the area of that portion of the paraboloid x=9-y^2-z^2
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