Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.5 The Divergence Theorem, #27 · Multivariable Calculus · Green, Stokes & divergence

(d) If … at all points then … at all points

True or false, with a good reason.

(a) If $\iint F \cdot n d S = 0$ for every closed surface, $F$ is constant.

(b) If $F = grad f$ then $\div F = 0$ .

(c) If $∣ F ∣ \leq 1$ at all points then $∭ \div F d V \leq$ area of the surface $S$ .

(d) If $∣ F ∣ \leq 1$ at all points then $∣ \div F ∣ \leq 1$ at all points.

~11 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.5 The Divergence Theorem, #27

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.