1. The surface S is obtained by rotating the curve y(u) = (cosh u, 0, u)...

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1. The surface S is obtained by rotating the curve y(u) = (cosh u, 0, u) around the z-axis in R. (a) Find a smooth parametrization o(u, v) of S. (b) Show that your parametrized surface o(u, v) in part (a) is regular. (c) Calculate the first fundamental form of the surface o(u, v) in part (a). 2. Let o(u, v) be a surface patch with standard unit normal N. a (a) Prove that where the matrix A = = ✓det (A) (Nxou) = Eo, - Fou EF (G) F G so that the first fundamental form of o(u, v) is (du, dv) A (du). (b) Find a similar formula for N x 0. 1. The surface S is obtained by rotating the curve y(u) = (cosh u, 0, u) around the z-axis in R. (a) Find a smooth parametrization o(u, v) of S. (b) Show that your parametrized surface o(u, v) in part (a) is regular. (c) Calculate the first fundamental form of the surface o(u, v) in part (a). 2. Let o(u, v) be a surface patch with standard unit normal N. a (a) Prove that where the matrix A = = ✓det (A) (Nxou) = Eo, - Fou EF (G) F G so that the first fundamental form of o(u, v) is (du, dv) A (du). (b) Find a similar formula for N x 0.

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a A smooth parametrization of the surface S can be given by ou v cosh u cos v cosh u sin v u ... View the full answer