Determine Whether or Not the Vector Field $\mathbf { F } ( x , y , z ) = z \mathbf { i } + 2 y z \mathbf { j } + \left( x + y ^ { 2 } \right) \mathbf { k }$

question 40

Essay

Determine whether or not the vector field $\mathbf { F } ( x , y , z ) = z \mathbf { i } + 2 y z \mathbf { j } + \left( x + y ^ { 2 } \right) \mathbf { k }$ is conservative. If it is conservative, find a function f such that $\mathbf { F } = \nabla f$ .

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