MediumWrite a proof

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #28 · Multivariable Calculus · Change of variables

The lines of length … and … meet at the angle

Problems, on the attraction of a sphere, use Figure 14.18 and the law of cosines $q^{2} = D^{2} - 2 ρ D cos ϕ + ρ^{2} = u$ .

The lines of length $D$ and $q$ meet at the angle $α$ . Move the meeting point up by $Δ D$ . Explain why the other line stretches by $Δ q \approx Δ D cos α$ . So $\partial q / \partial D = cos α$ as before.

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #28

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.