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Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for 0 in [0, 2n] and ø in [0, n]. 2 cos(0) sin($), 3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2($) + 4 2 cos(0) sin(4), -3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), –3 sin(0) sin(4), –6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), 3 sin(0) sin(4), -6 cos(4)) 5 sin?(0) sin?(4) + 32 cos?($) + 4 -3 cos(0) sin(4), -2 sin(0) sin($), -6 cos(4) V5 sin?(0) sin?($) + 32 cos2(4) + 4 CoS Identify this surface. sphere ellipsoid cylinder circular parabaloid elliptical parabaloid

Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for 0 in [0, 2n] and ø in [0, n]. 2 cos(0) sin($), 3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2($) + 4 2 cos(0) sin(4), -3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), –3 sin(0) sin(4), –6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), 3 sin(0) sin(4), -6 cos(4)) 5 sin?(0) sin?(4) + 32 cos?($) + 4 -3 cos(0) sin(4), -2 sin(0) sin($), -6 cos(4) V5 sin?(0) sin?($) + 32 cos2(4) + 4 CoS Identify this surface. sphere ellipsoid cylinder circular parabaloid elliptical parabaloid

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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Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for 0 in [0, 2n] and ø in [0, n]. 2 cos(0) sin($), 3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2($) + 4 2 cos(0) sin(4), -3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), –3 sin(0) sin(4), –6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), 3 sin(0) sin(4), -6 cos(4)) 5 sin?(0) sin?(4) + 32 cos?($) + 4 -3 cos(0) sin(4), -2 sin(0) sin($), -6 cos(4) V5 sin?(0) sin?($) + 32 cos2(4) + 4 CoS Identify this surface. sphere ellipsoid cylinder circular parabaloid elliptical parabaloid
Transcribed Image Text:Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for 0 in [0, 2n] and ø in [0, n]. 2 cos(0) sin($), 3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2($) + 4 2 cos(0) sin(4), -3 sin(0) sin($), 6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), –3 sin(0) sin(4), –6 cos(4) 5 sin?(0) sin?(4) + 32 cos2(4) + 4 -2 cos(0) sin($), 3 sin(0) sin(4), -6 cos(4)) 5 sin?(0) sin?(4) + 32 cos?($) + 4 -3 cos(0) sin(4), -2 sin(0) sin($), -6 cos(4) V5 sin?(0) sin?($) + 32 cos2(4) + 4 CoS Identify this surface. sphere ellipsoid cylinder circular parabaloid elliptical parabaloid
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