(b) Consider the surface s = {(x,y.2) E R°Ix² +y² +z² = 13 and z>2} and assume that S is oriented upward. Let C be the oriented boundary of S. Sketch the set S in R³ and show the oriented curve C on the sketch. (i) (ii) Find a parametric equation for C. (ii) Let F(x, y,z)= (y,-x,2z). Use Stokes' Theorem to evaluate the flux integral ſ Ccurl F) n ds
(b) Consider the surface s = {(x,y.2) E R°Ix² +y² +z² = 13 and z>2} and assume that S is oriented upward. Let C be the oriented boundary of S. Sketch the set S in R³ and show the oriented curve C on the sketch. (i) (ii) Find a parametric equation for C. (ii) Let F(x, y,z)= (y,-x,2z). Use Stokes' Theorem to evaluate the flux integral ſ Ccurl F) n ds
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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Transcribed Image Text:QUESTION 8
(b) Consider the surface
s = {(x,y, z) E R°Ix² +y² +z² = 13 and z22}
and assume that S is oriented upward.
Let C be the oriented boundary of S.
Sketch the set S in R³ and show the oriented curve C on the sketch.
(1)
(ii)
Let F(x, y, z)= (y,-x,2z). Use Stokes' Theorem to evaluate the flux
Find a parametric equation for C.
(ii)
integral
ſ Caurl F) n ds
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