Estimating Div \vec{F} at (2, 9, 11): A Tutorial

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Homework Statement

A vector field $$\vec{F}$$ has the property that the flux of $$\vec{F}$$ out of a small cube of side 0.01 centered around the point (2, 9, 11) is 0.003. Estimate div$$\vec{F}$$ at the point (2, 9, 11).

Homework Equations

The Attempt at a Solution

can someone please help me how to solve this...

 

[dx]

For a small volume ∆V, the flux of F out of the region is approximately equal to (∇⋅F)∆V. Use Gauss' divergence theorem to see this.