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
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?($) + 32 cos2(4) + 4
CoS
Identify this surface.
sphere
ellipsoid
cylinder
circular parabaloid
elliptical parabaloid](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19331858-c67c-414f-8328-5459040eae8a%2Fa4ea04d6-8c10-4ffe-bcd4-096df935c276%2Fjvum8tq.png&w=3840&q=75)
Transcribed Image Text:Consider the following surface parametrization.
x = 3 cos(0) sin(4),
y = 2 sin(0) sin(4),
cos(4)
Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for 0 in [0, 2n] and ø in [0, n].
2 cos(0) sin($), 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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