4) Let S be a parametrized surface given by the parametrization X (u, v) = (u...

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4) Let S be a parametrized surface given by the parametrization X (u, v) = (u cos v, u sin v, 3v), (a helicoid). Find a) the Gaussian and mean curvature of the surface X, b) dN,, where N is the Gauss map, c) principal curvatures, d) normal curvature k, of the surface in the direction of the curve u = 2+ v. 4) Let S be a parametrized surface given by the parametrization X (u, v) = (u cos v, u sin v, 3v), (a helicoid). Find a) the Gaussian and mean curvature of the surface X, b) dN,, where N is the Gauss map, c) principal curvatures, d) normal curvature k, of the surface in the direction of the curve u = 2+ v.