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Give a parametric representation r of the spherical cap left when the sphere 2² + y² +2²=8 is cut by the plane z = -2, using spherical coordinates. Take the cap with => 0. Give a parametric representation r of the surface cut from the parabolic cylinder y=z² by the planes z = 0, z = 3 and y = 2. Give a parametric representation of the ellipsoid using spherical coordinates. (-)² + (H)² + (-)² = ¹ 1

Give a parametric representation r of the spherical cap left when the sphere 2² + y² +2²=8 is cut by the plane z = -2, using spherical coordinates. Take the cap with => 0. Give a parametric representation r of the surface cut from the parabolic cylinder y=z² by the planes z = 0, z = 3 and y = 2. Give a parametric representation of the ellipsoid using spherical coordinates. (-)² + (H)² + (-)² = ¹ 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Give a parametric representation r of the spherical cap left when the sphere x² + y² +2²=8 is cut by the plane z = -2, using spherical coordinates. Take the cap with z > 0. b) Give a parametric representation r of the surface cut from the parabolic cylinder y = z² by the planes z = 0, z = 3 and y = c) Give a parametric representation of the ellipsoid using spherical coordinates. 2 2 ( ² ) ² + ( 1 )² + ( ² ) ² = ¹ 1
Transcribed Image Text:a) Give a parametric representation r of the spherical cap left when the sphere x² + y² +2²=8 is cut by the plane z = -2, using spherical coordinates. Take the cap with z > 0. b) Give a parametric representation r of the surface cut from the parabolic cylinder y = z² by the planes z = 0, z = 3 and y = c) Give a parametric representation of the ellipsoid using spherical coordinates. 2 2 ( ² ) ² + ( 1 )² + ( ² ) ² = ¹ 1
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