Calculus 3 Quiz
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VECTOR FIELDS & LINE/SURFACE INTEGRALS
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A vector field F(x,y,z)\mathbf{F}(x,y,z) satisfies div(F)=x2+y2+z2\text{div}(\mathbf{F}) = x^2 + y^2 + z^2 and curl(F)⋅k=xy\text{curl}(\mathbf{F}) \cdot \mathbf{k} = xy, where k\mathbf{k} is the unit vector in the zz-direction. If F=(P,Q,R)\mathbf{F} = (P, Q, R) and ∂P∂x=x2\frac{\partial P}{\partial x} = x^2, what is ∂Q∂y+∂R∂z\frac{\partial Q}{\partial y} + \frac{\partial R}{\partial z}?
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