Consider the 3-dimensional vector field F defined by F(x,y,z)=(2xyz,x²z+2yz²,x²y+2y²z+e^z).
1.write down the Jacobian matrix jf(x,y,z).
2.determine divF (x,y,z).
3.determine curl F (x,y,z).
4.does F have a potential function? Give reasons for your answer, referring to the relevant definitions and theorems in the study guide.
5.find a potential function of F .
1.
Jacobian Matrix
2.
3.
4. Let be a vector field in space on a simply connected domain. If then is conservative.
There exists a function such that In this situation is called
a potential function for
5.
A potential function of F is
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