Multivariable Calculus Quiz
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VECTOR FIELDS
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Let F(x,y,z)=⟨x3+sin⁡(z),y3+cos⁡(z),R(x,y,z)⟩\mathbf{F}(x,y,z) = \langle x^3 + \sin(z), y^3 + \cos(z), R(x,y,z) \rangle. If the vector field F\mathbf{F} is incompressible (i.e., has zero divergence everywhere), which of the following could be the component R(x,y,z)R(x,y,z)?
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