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

Expert Solution

Colby Messinger answered 1 year ago

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)+2y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2y+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.

Question

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

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Expert Solution

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