Let S be the surface with parametrization F(u, v) = (V1+ u² cos v, /1+ u² sin v, u), 0< u< 1,0 < v < 27. %3D S is a piece of a quadric surface. Determine the equation (in x,y and z) for this quadric and use this knowledge to sketch S. Compute the outward flux of the vector field F(x,y, z) = (/x² + y², /x² + y², z) across S. utward means "away from the z-axis".) %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 2. Let S be the surface with parametrization
F(u, v) = (/1+u² cos v, /1+ u² sin v, u), 0<u< 1,0 < v < 2n.
%3D
(a)
surface, and use this knowledge to sketch S.
S is a piece of a quadric surface. Determine the equation (in x,y and z) for this quadric
(b)
Compute the outward flux of the vector field F(x,y, z) = (/² + y², /x² + y², z) across S.
(Here outward means "away from the z-axis".)
Transcribed Image Text:Question 2. Let S be the surface with parametrization F(u, v) = (/1+u² cos v, /1+ u² sin v, u), 0<u< 1,0 < v < 2n. %3D (a) surface, and use this knowledge to sketch S. S is a piece of a quadric surface. Determine the equation (in x,y and z) for this quadric (b) Compute the outward flux of the vector field F(x,y, z) = (/² + y², /x² + y², z) across S. (Here outward means "away from the z-axis".)
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