Question

Use Green's Theorem to find the counterclockwise circulation and outward flux for the field

F=(3x−y)i+(y−x)j and curve C: the square bounded by x=0, x=4,y=0, y=4.

find flux and circulation

Answer #1

Use Green's theorem to find the counterclockwise circulation and
outward flux for the field F=(4x-9y)i +(8y-9x)j and the curve C:
the triangle bounded by x=0,x=8,y=0 ,y=8 The flux is ??? The
circulation is ???

Calculate the outward flux of the vector field F(x,y) =
x[i] + y^2[j] across the square
bounded by x= 1, x= -1, y=
1 and y= -1.

8. Use the Divergence Theorem to compute the net outward flux of
the field F= <-x, 3y, z> across the surface S, where S is the
surface of the paraboloid z= 4-x^2-y^2, for z ≥ 0, plus its base in
the xy-plane.
The net outward flux across the surface is ___.
9. Use the Divergence Theorem to compute the net outward flux of
the vector field F=r|r| = <x,y,z> √x^2 + y^2 + z^2 across the
boundary of the region...

Use the Divergence Theorem to evaluate
F.N dS
and find the outward flux of F through the surface of the
solid bounded by the graphs of the equations.
F(x, y, z) = xi + xyj + zk
Q: solid region bounded by the coordinate planes and the plane
3x + 4y + z = 24

Use the Divergence Theorem to evaluate
S
F · N dS
and find the outward flux of F through the
surface of the solid bounded by the graphs of the equations.
F(x, y,
z) =
x2i +
xyj +
zk
Q: solid region bounded by the coordinate
planes and the plane 3x + 5y +
6z = 30

Use the Divergence Theorem to evaluate
S
F · N dS
and find the outward flux of F through the
surface of the solid bounded by the graphs of the equations.
F(x, y,
z) =
x2i +
xyj +
zk
Q: solid region bounded by the coordinate
planes and the plane 3x + 4y +
6z = 24

Use the Divergence Theorem to find the outward flux of F=9y
i+5xy j−6z k
across the boundary of the region D: the region inside the
solid cylinder x2+y2≤4 between the plane z=0
and the paraboloid z=x2+y2
The outward flux of F=9y i+5xy
j−6z k across the boundry of
region D is____

Use the divergence theorem to find the outward flux ∫ ∫ S
F · n dS of the vector field F = cos(10y + 5z) i + 9 ln(x2 +
10z) j + 3z2 k, where S is the surface of the region bounded
within by the graphs of z = √ 25 − x2 − y2 , x2 + y2 = 7,
and z = 0. Please explain steps. Thank you :)

Stokes' Theorem is the generalization of the circulation form of
Green's Theorem in the x y-plane. Use Stokes' Theorem to write the
circulation form of Green's Theorem in the y z-plane.

Stokes' Theorem is the generalization of the circulation form of
Green's Theorem in the x y-plane. Use Stokes' Theorem to write the
circulation form of Green's Theorem in the y z-plane.
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