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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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.
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