Question: Let (mathbf{F}) be a vector field whose curl and divergence at the origin are [ operatorname{curl}(mathbf{F})(0,0,0)=langle 2,-1,4angle, quad operatorname{div}(mathbf{F})(0,0,0)=-2 ] Estimate (oint_{mathcal{C}} mathbf{F} cdot d

Let $\mathbf{F}$ be a vector field whose curl and divergence at the origin are

\[
\operatorname{curl}(\mathbf{F})(0,0,0)=\langle 2,-1,4angle, \quad \operatorname{div}(\mathbf{F})(0,0,0)=-2
\]

Estimate $\oint_{\mathcal{C}} \mathbf{F} \cdot d \mathbf{r}$, where $C$ is the circle of radius 0.03 in the $x y$-plane centered at the origin.

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