Determine whether or not the vector field is conservative. If it is, find a potential function. $$\left\langle y^{2} z^{2}-1,2 x y z^{2}, 4 z^{3}\right\rangle$$
Added by James A.
Step 1
To do this, we can use the curl test. If the curl of the vector field is zero, then the field is conservative. $$\nabla \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & Show more…
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