1. Calculate the second fundamental form of the parametric surface given by x(u, v) = ( u cos v, u sin v, u^(2) ). 2. calculate the Gaussian curvature K of the parametric surface given by x(u, v) = (u, e^(u) cos v, e^(u) sin v) 3. Let x(u, v) = (u+v, u-v, u*v) be the parametrization of a surface. Calculate the mean curvature H.

1. Calculate the second fundamental form of the parametric surface given by x(u, v) = ( u cos v, u sin v, u^(2) ). 2. calculate the Gaussian curvature K of the parametric surface given by x(u, v) = (u, e^(u) cos v, e^(u) sin v) 3. Let x(u, v) = (u+v, u-v, u*v) be the parametrization of a surface. Calculate the mean curvature H.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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