(b) Consider the surface s = {(x,y,2) € R°Ix* +y² +z* =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. (ii) Find a parametric equation for C. (ii) Let F(x, y, =)=(y,-x,2z). Use Stokes' Theorem to evaluate the flux integral ([ (curl F) n dS
(b) Consider the surface s = {(x,y,2) € R°Ix* +y² +z* =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. (ii) Find a parametric equation for C. (ii) Let F(x, y, =)=(y,-x,2z). Use Stokes' Theorem to evaluate the flux integral ([ (curl 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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(b) Consider the surface
s= {x,y,2) € R°lx° + y² +z* = 13 and z22}
and assume that S is oriented upward.
Let C be the oriented boundary of S.
(i)
Sketch the set Sin R³ and show the oriented curve C on the sketch.
(ii)
Find a parametric equation for C.
(i)
Let F(x, y,z)=(y,-x,2z). Use Stokes' Theorem to evaluate the flux
integral
f (curl F) n ds
W
ll
11:42 AM
2021-10-06
Page: 1 of 1
110% -
+
Words: 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94ea00a2-f5ad-495c-94c7-735caa6aac17%2F52a6e4fa-bc37-4fa4-854b-d69f383b8290%2Fhx65m2f_processed.png&w=3840&q=75)
Transcribed Image Text:Document1 - Microsoft Word (Product Activation Failed)
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L'2·!'1'L:X::1:I'2•I ' 3: 1' 4• I:5'1'6'L:7'1'8 I9'1' 10. 1' 11· I'12. 1' 13 ·L'14· I ' 15' LA:L17 |' 18.
(b) Consider the surface
s= {x,y,2) € R°lx° + y² +z* = 13 and z22}
and assume that S is oriented upward.
Let C be the oriented boundary of S.
(i)
Sketch the set Sin R³ and show the oriented curve C on the sketch.
(ii)
Find a parametric equation for C.
(i)
Let F(x, y,z)=(y,-x,2z). Use Stokes' Theorem to evaluate the flux
integral
f (curl F) n ds
W
ll
11:42 AM
2021-10-06
Page: 1 of 1
110% -
+
Words: 0
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