Question

Let S be the portion of the surface z=cos(y) with 0≤x≤4 and -π≤y≤π. Find the flux of F=<e^-y,2z,xy> through S:

∫∫F*n dS

Answer #1

Find the tangent plane to the surface z = cos(xy) when (x, y) =
(π, 0).

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

Problem 10. Let F = <y, z − x, 0> and let S be the surface
z = 4 − x^2 − y^2 for z ≥ 0, oriented by outward-pointing normal
vectors.
a. Calculate curl(F).
b. Calculate Z Z S curl(F) · dS directly, i.e., evaluate it as a
surface integral.
c. Calculate Z Z S curl(F) · dS using Stokes’ Theorem, i.e.,
evaluate instead the line integral I ∂S F · ds.

Let F ( x , y , z ) =< e^z sin( y ) + 3x , e^x cos( z ) + 4y
, cos( x y ) + 5z >, and let S1 be the sphere x^2 + y^2 + z^2 =
4 oriented outwards Find the flux integral ∬ S1 (F) * dS. You may
with to use the Divergence Theorem.

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.

Evaluate the flux, ∬SF⋅dS , of F(x,y,z)=yzj+z^2k through the
surface of the cylinder y^2+z^2=9 , z ≥ 0 , between the planes x=0
and x=3.

Let S be the surface z = m + x^2 + y^2 above the rectangle [0,
3] x [0, 4].
Compute the flux of the vector field F(x, y, z) = 4 x i + 2 y j
+ 4 z k across S.
Your answer should be an exact expression.
Please help me I need this ASAP

4.Given F(x,y,z)=(cos(y))i+(sin(y))j+k, find divF and curlF at
P0(π/4,π,0) divF(P0)=? curlF(P0)= ?

Compute the surface integral of F(x, y, z) = (y,z,x) over the
surface S, where S is the portion of the cone x = sqrt(y^2+z^2)
(orientation is in the negative x direction) between the planes x =
0, x = 5, and above the xy-plane.
PLEASE EXPLAIN

Let f(x, y) =sqrt(1−xy) and consider the surface S defined by
z=f(x, y).
find a vector normal to S at (1,-3)

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