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Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the sphere x² + y² + z² = 3 Use the parameterization r(z,0) = (√1 + z² cos 0, √1 + z² sin 0,z) with appropriate lim- its to compute F.ds where F(x, y, z) = (y, -x, -z).

Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the sphere x² + y² + z² = 3 Use the parameterization r(z,0) = (√1 + z² cos 0, √1 + z² sin 0,z) with appropriate lim- its to compute F.ds where F(x, y, z) = (y, -x, -z).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the sphere x² + y² + z² = 3 Use the parameterization r(z,0) = (√1 + z² cos 0, √1 + z² sin 0,z) with appropriate lim- its to compute SF F.ds where F(x, y, z) = (y, -x, -z).
Transcribed Image Text:Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the sphere x² + y² + z² = 3 Use the parameterization r(z,0) = (√1 + z² cos 0, √1 + z² sin 0,z) with appropriate lim- its to compute SF F.ds where F(x, y, z) = (y, -x, -z).
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