Question

Use the Divergence Theorem to compute the net outward flux of the field F equalsleft angle negative 4 x comma font size decreased by 6 y comma font size decreased by 6 7 z right angle across the surface S, where S is the sphere StartSet left parenthesis x comma y comma z right parenthesis : x squared plus y squared plus z squared equals 6 EndSet.

Answer #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...

Consider the following region R and the vector field F. a.
Compute the two-dimensional divergence of the vector field. b.
Evaluate both integrals in Green's Theorem and check for
consistency. Bold Upper F equals left angle x comma y right angle ;
Upper R equals left parenthesis x comma y right parenthesis : x
squared plus y squared less than or equals 9

Use the divergence theorem to find the outward flux of F across
the boundary of the region D.
F =x^2i -2xyj + 5xzk
D: The region cut from the first octant by the sphere
x^2+y^2+z^2=1

Use the divergence theorem to find the outward flux (F · n) dS S
of the given vector field F. F = y2i + xz3j + (z − 1)2k; D the
region bounded by the cylinder x2 + y2 = 25 and the planes z = 1, z
= 6

Use the Divergence Theorem to find the outward flux of F = 3yi
+7xyj-2zk across the boundary of the region D: the region inside
the solid cylinder x^2 + y^2 less than or equal to 4 between the
plane z=0 and the paraboloid z = x^2 + y^2.

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.

. a. [2] Compute the divergence of vector field F = x 3y 2 i +
yj − 3zx2y 2k
b. [7] Use divergence theorem to compute the outward flux of the
vector field F through the surface of the solid bounded by the
surfaces z = x 2 + y 2 and z = 2y

Use Stokes’ Theorem to calculate the flux of the curl of the
vector field F = <y − z, z − x, x + z> across the surface S
in the direction of the outward unit normal where S : r(u, v)
=<u cos v, u sin v, 9 − u^2 >, 0 ≤ u ≤ 3, 0 ≤ v ≤ 2π. Draw a
picture of S.

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 calculate the surface integral
S
F · dS;
that is, calculate the flux of F across
S.
F(x, y, z) = ey
tan(z)i + y
3 − x2
j + x sin(y)k,
S is the surface of the solid that lies above the
xy-plane and below the surface
z = 2 − x4 − y4,
−1 ≤ x ≤ 1,
−1 ≤ y ≤ 1.

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