Question
In: Advanced Math
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and
F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and
F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j...
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 -
y^2)j + (x^2 + y^2 - z^2)k over the portion of the surface x^2 +
y^2 -2ax + az = 0
Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...
Verify the Divergence Theorem for the vector field F(x, y, z) =
< y, x , z^2 > on the region E bounded by the planes y + z =
2, z = 0 and the cylinder x^2 + y^2 = 1.
By Surface Integral:
By Triple Integral:
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2...
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x,
y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the
paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 =
4, oriented upwards. Sketch the surface S and label everything.
Verify the Divergence Theorem for the vector eld F(x; y; z) = hy; x; z2i on...
Verify the Divergence Theorem for the vector eld
F(x; y; z) = hy; x; z2i on the region E bounded by the planes y
+ z = 2,
z = 0 and the cylinder x2 + y2 = 1.
Surface Integral:
Triple Integral:
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find
the flux of F across S, the part of the paraboloid x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2...
1A) Use surface integral to evaluate the flux
of
F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2
1B) Use the Divergence Theorem to evaluate the
flux of F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z)...
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two
constraints x+y+z=6 and x-2*y+z=0. find the extreme value of
f(x,y,z) and determine whether it is maximum of minimum.
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi...
Use the Divergence Theorem to evaluate
S
F · dS,
where
F(x, y,
z) =
z2xi
+
y3
3
+ cos z
j +
(x2z +
y2)k
and S is the top half of the sphere
x2 +
y2 + z2 =
4.
(Hint: Note that S is not a closed surface.
First compute integrals over S1 and
S2, where S1 is the
disk
x2 +
y2 ≤ 4,
oriented downward, and S2 =
S1 ∪ S.)
F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z...
F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the
paraboloid z = x^2+y^2that lies inside the cylinder x^2+y^2 = 16,
oriented upward.
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