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For each surface below, give a parameterization r(u, v); be sure to use rectangular bounds (u, v) € [a, b] x [c, d], and specify the bounds. For full credit, it is enough to find any three of the four parameterizations; for extra credit, find all four. An upside-down cone of height 3 with its tip on the origin and a circular base of radius 1 parallel to the xy-plane. The portion of the parabola z = x²+y2 above the plane z = 1 and below the plane z = 4. The portion of the plane 2x + 3y+4z = 5 where 0 ≤ y ≤1 and 0≤ Z ≤1. A sphere of radius 1 centered at the point (1,2,-3).

For each surface below, give a parameterization r(u, v); be sure to use rectangular bounds (u, v) € [a, b] x [c, d], and specify the bounds. For full credit, it is enough to find any three of the four parameterizations; for extra credit, find all four. An upside-down cone of height 3 with its tip on the origin and a circular base of radius 1 parallel to the xy-plane. The portion of the parabola z = x²+y2 above the plane z = 1 and below the plane z = 4. The portion of the plane 2x + 3y+4z = 5 where 0 ≤ y ≤1 and 0≤ Z ≤1. A sphere of radius 1 centered at the point (1,2,-3).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 35E
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For each surface below, give a parameterization r(u, v); be sure to use rectangular bounds (u, v) € [a, b] x [c, d], and specify the bounds. For full credit, it is enough to find any three of the four parameterizations; for extra credit, find all four. An upside-down cone of height 3 with its tip on the origin and a circular base of radius 1 parallel to the xy-plane. The portion of the parabola z = x²+y2 above the plane z = 1 and below the plane z = 4. The portion of the plane 2x + 3y+4z = 5 where 0 ≤ y ≤1 and 0≤ Z ≤1. A sphere of radius 1 centered at the point (1,2,-3).
Transcribed Image Text:For each surface below, give a parameterization r(u, v); be sure to use rectangular bounds (u, v) € [a, b] x [c, d], and specify the bounds. For full credit, it is enough to find any three of the four parameterizations; for extra credit, find all four. An upside-down cone of height 3 with its tip on the origin and a circular base of radius 1 parallel to the xy-plane. The portion of the parabola z = x²+y2 above the plane z = 1 and below the plane z = 4. The portion of the plane 2x + 3y+4z = 5 where 0 ≤ y ≤1 and 0≤ Z ≤1. A sphere of radius 1 centered at the point (1,2,-3).
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