Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 64


Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 64 <x? + y? <81.<br>Choose the normal vector n to the surface which has positive third component.<br>A) Give a parametrization of S in terms of the variables r,0 from cylindrical coordinates<br>r(r,0) = (], II)<br>%3D<br>y<br>VZ).<br>y2<br>B) Consider the vector field F = (-<br>Vx? +y?<br>+<br>Write a double integral in terms of r,0 which computes the flux of F across S:<br>02 r2<br>Flux=<br>dr de<br>01 r1<br>01 =<br>02 =<br>r1=<br>r2=<br>

Extracted text: Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 64 <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="">

Jun 03, 2022
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