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a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a conservative vector field? Justify. b. Is F incompressible? Explain. Is it...

a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a conservative vector field? Justify.

b. Is F incompressible? Explain. Is it irrotational? Explain.

c. The vector field F(x,y,z)= < 6xy^2+e^z, 6yx^2 +zcos(y),sin(y)xe^z > is conservative. Find the potential function f. That is, the function f such that ▽f=F. Use a process.

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