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Multivariable & Vectorhard
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For what value of the constant kkk is the vector field F⃗=⟨kxy+z3,x2+2yz,y2+3xz2⟩\vec{F} = \langle k xy + z^3, x^2 + 2yz, y^2 + 3xz^2 \rangleF=⟨kxy+z3,x2+2yz,y2+3xz2⟩ conservative in all of R3\mathbb{R}^3R3?