Consider the surface S consisting of the portion the graph of the function z = x2 + y² above the annulus 64 sx2 + y² s 81. 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) = y B) Consider the vector field F = x² + y² Vx? + y² 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=
Consider the surface S consisting of the portion the graph of the function z = x2 + y² above the annulus 64 sx2 + y² s 81. 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) = y B) Consider the vector field F = x² + y² Vx? + y² 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=
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 = x2 + y? above the annulus 64 <x? + y? <81.
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) = (], II)
%3D
y
VZ).
y2
B) Consider the vector field F = (-
Vx? +y?
+
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=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f8b034a-4c7c-470d-9618-23bab9c015a9%2Fc7c29f2a-3e18-4d6c-ae63-3b80175bb48a%2F4df1sg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 64 <x? + y? <81.
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) = (], II)
%3D
y
VZ).
y2
B) Consider the vector field F = (-
Vx? +y?
+
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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