Problem 4422

Problems in Mathematical Analysis · 8.17

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Problem 4422

Prove

\operatorname {div}\overrightarrow {a}(M) = \lim _{d(S)\to 0} \dfrac {1}{V}\iint _{S} \overrightarrow {a}\cdot \overrightarrow {n}\, dS ,

where $S$ is a closed surface enclosing the point $M$ and bounding a volume $V$ , $\overrightarrow {n}$ is the outward normal of the surface $S$ , and $d(S)$ is the diameter of the surface $S$ .

Problem 4422.1

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