Question

Find the flux of the vector field F(x, y, z) = x, y, z through the portion of the parabaloid z = 16 - x^2-y^2 above the plane ? = 7 with upward pointing normal.

Answer #1

Find the flux of the vector field F =
x i +
e6x j +
z k through the surface S given
by that portion of the plane 6x + y +
3z = 9 in the first octant, oriented upward.
PLEASE EXPLAIN STEPS. Thank you.

Find the flux of the vector field F (x, y, z) =< y, x, e^xz
> outward from the z−axis and across the surface S, where S is
the portion of x^2 + y^2 = 9 with x ≥ 0, y ≥ 0 and −3 ≤ z ≤ 3.

PLEASE explain STEPS. Thank you :)
Find the flux of the vector field F =
x i +
e6x j +
z k through the surface S given
by that portion of the plane 6x + y +
3z = 9 in the first octant, oriented upward. (a clear
explained answer would be appreciated)

. Find the flux of the vector field F~ (x, y, z) =
<y,-x,z> over a surface with downward orientation, whose
parametric equation is given by r(s, t) = <2s, 2t, 5 − s 2 − t 2
> with s^2 + t^2 ≤ 1

Use Stokes' Theorem to compute the flux of
curl(F) through the
portion of the plane x37+y33+z=1 where
x, y, z≥0, oriented with an
upward-pointing normal, for F = <yz,
0, x>.
(Use symbolic notation
and fractions where needed.)
Flux =

Use Stokes' Theorem to compute the flux of curl(F) through the
portion of the plane x37+y33+z=1 where x, y, z≥0, oriented with an
upward-pointing normal, for F = <yz, 0, x>.
(Use symbolic notation and fractions where needed.)
Flux =

Use the divergence theorem to calculate the flux of the vector
field F = (y +xz) i+ (y + yz) j - (2x + z^2) k upward through the
first octant part of the sphere x^2 + y^2 + z^2 = a^2.

Set up a double integral to find the flux of the vector field F
= <−x, −y, z^3 > through the surface S, where S is the part
of the cone z = sqrt( x^2 + y^2) between z = 1 and z = 3. You do
not have to evaluate the double integral.

Let σ be the portion of the surface z = 1−x^2 −y^2 that lies
above the xy-plane, and suppose that σ is oriented upward, as
shown. Find the flux of the vector field F(x, y, z) = 〈x, y, 2z〉
across σ. BOX your answer

Compute ∫∫S F·dS for the vector field F(x,y,z)
=〈0,0,x2+y2〉through the surface given by x^2+y^2+z^2= 4, z≥0 with
outward pointing normal.
Please explain and show work.
Thank you so much.

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