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Consider the surface s = {(x,y.2) € R°|x* + 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 R' and show the oriented curve C on the sketch. (1) Find a parametric equation for C. (ii) Let F(x, y,z)=(y.-x,2z). Use Stokes' Theorem to evaluate the flux (ii) integral JI (curl E) n dS

Consider the surface s = {(x,y.2) € R°|x* + 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 R' and show the oriented curve C on the sketch. (1) Find a parametric equation for C. (ii) Let F(x, y,z)=(y.-x,2z). Use Stokes' Theorem to evaluate the flux (ii) integral JI (curl E) n dS

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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Transcribed Image Text:Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - Calibri (Body) - 11 - A A Aa AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace IU - abe X, x* I Normal I No Spaci. Heading 1 Change Styles W Paste B Heading 2 Title Subtitle A Select - Format Painter Clipboard Font Paragraph Styles Editing 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 ={(x,y,z) € R³I x² +y² + z? =13 and :22} and assume that S is oriented upward. Let C be the oriented boundary of S. (i) Sketch the set Sin R and show the oriented curve C on the sketch. (ii) Find a parametric equation for C (iii) Let F(x, y,z)= (y.– x, 2z). Use Stokes' Theorem to evaluate the flux integral (сurl F) n ds ll 02:01 PM 2021-10-06 Page: 1 of 1 110% - +) Words: 0
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