# Vector field divergence equivalent definition

Mathematics Asked by user_hello1 on August 13, 2020

Could someone direct me to a proof showing the equivalence between the following two definitions of the divergence of vector field $$F$$ at $$x$$? (1) $$lim_{|V| to 0} cfrac{alpha({S})}{|V|}$$, where $$alpha$$ is the surface integral of $$F$$ over surface $$S$$ with volume $$V$$ containing $$x$$ (2) $$cfrac{partial F_1}{partial x_1} + dots + cfrac{partial F_n}{partial x_n}$$; the first makes intuitive sense to me, the second not at all.

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