Question

Let S be the parabolid x^2+y^2+z = R^2 , 0 11 years ago

Answer 1

I'm gonna use the formula : \[\int\limits F (x, y, f(x,y)) * (-f_x - f_y +k ) dx dy \]

Answer 2

so I have \[(−fx−fy+k)dxdy = (-2 x i - 2yj +k)dxdy\]

Answer 3

so what would \[F(x,y,f(x,y))\] be ?

Answer 4

\[F(x i + yj + (-x-y+R)k) ???\]

Answer 5

\[\nabla\]

Answer 6

Thank you!

Answer 7

so I take the gradient F?

Answer 8

\[\vec F = \nabla f\]

yes.

Answer 9

\(\ \nabla\) @Jhannybean :P

Answer 10

nevermind...

Answer 11

gradient is i + j + 2zk

Answer 12

so i sub in \[F⃗ =∇f\] on my formula?

Answer 13

You are like 3 sections ahead of me!! Haha, I'm working on Stokes' and Divergent Theorem atm :(

Answer 14

meet too

Answer 15

i suppose to use the general formula to find the flux for this problem

Answer 16

Isn't flux : \[\int\int_S \vec F \cdot dS = \int\int_S = \vec F \cdot \vec n dS\]

Answer 17

\[\vec n = \frac{|\nabla f |}{\sqrt{| \nabla f|}}\]

Answer 18

yeah but why would i need the unit normal?

Answer 19

@dan815

Answer 20

et S be the parabolid x^2+y^2+z +R^2 , 0<z<R^2, oriented upward and let F = xi + yj +z^2k. find the flux of the vector field F through the surface S.

Answer 21

x^2+y^2+z =R^2 ?

Answer 22

yeah = R^2 sorry

Answer 23

I edit the question

Answer 24

ok

Answer 25

do div F dv

Answer 26

uh

Answer 27

wrong surface

Answer 28

-z=x^2+y^2-r^2