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Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 4

Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 4

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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Consider the surface S consisting of the portion of the graph of the function z = x? + y above the annulus 4<x? +y <9. Choose the normal vector n to the surface which has positive third component. A) Give a parametrization of S in terms of the variables r,0 from cylindrical coordinates r(r,0) = (O,I I) y VZ). +y? B) Consider the vector field F = Write a double integral in terms of r,0 which computes the flux of F across S: 02 r2 Flux= dr de 01 r1 01 = 02 = r1= r2=
Transcribed Image Text:Consider the surface S consisting of the portion of the graph of the function z = x? + y above the annulus 4<x? +y <9. Choose the normal vector n to the surface which has positive third component. A) Give a parametrization of S in terms of the variables r,0 from cylindrical coordinates r(r,0) = (O,I I) y VZ). +y? B) Consider the vector field F = Write a double integral in terms of r,0 which computes the flux of F across S: 02 r2 Flux= dr de 01 r1 01 = 02 = r1= r2=
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