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.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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