Use the Divergence Theorem to compute the net outward flux of the field F = (-x,4y,z) across the surface S, where S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z = 3. The net outward flux across the boundary of the tetrahedron is (Type an exact answer, usingn as needed.)

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (2x,3y,2z) across the…

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Q: Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector…

A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E…

Q: Use the Divergence Theorem to compute the net outward flux of the field F=(2x, 3y, -z)  across the…

A: To calculate the net outward flux of the given vector field across the given surface

Q: Use the divergence theorem to calculate the flux of the vector field F(x,y, z) = 2xyi + z8 j + 6yk…

A: Divergence Theorem:      ∬F→·dA→    = ∬∫∇·F→dv       s                       v

Q: Find the counterclockwise circulation and outward flux of the field F = xyi + 4yʻj around and over…

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Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (x + z², xz + y² , zx – y)…

A: The vector field is Fx, y, z=x+z2, xz+y2, zx-y Divergence theorem: ∬SF·dS=∭VdivFdV Obtain the…

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = 5xyi + z°j+9yk…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z) across…

A: Given vector field F=x2,-y2,z2 D is the region in the first octant between the planes z=8-x-y and…

Q: Use the divergence theorem to compute the flux integral P F . în ds where n is the outward pointing…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

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Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: Evaluate the line integral of the vector field F(x, y, z) = (x²y³, e™y+z, x+ z²) around the circle…

A: Solution is as below

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

Q: Consider the surface integral of the vector field F = [xy?, 3x², x²z] over a surface S, where S…

A: We will use of gauss divergence theorem

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (4x…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2,…

A: The vector field is given as

Q: Find the flux of the field F =-x i - y j + z2 k outward (normal away from the z-axis) through the…

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Q: Consider the vector field F = a?i+ ?j+ y²k Calculate the divergence: Calculate the curl, Suppose S…

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: find the work done by the given vector field F along the specified curve C.   F(x, y) = yi − x j,…

A: Given, F(x,y)=yi^-xj^ where curve, x2+y2=4 W=∫F.dr W=∫ydx-xdy from curve, dx=-dy W=∫xdx+ydy limit of…

Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (e²²,5y + sin (x² z), 8z +…

A: To find:- The flux of the field F through surface S Concept Used:- The flux of the field F through…

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (- 2x,y, - 2z) across…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

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Q: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

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Q: 12. Use a parameterization to find the flux across the surface cut from the cylinder x? + y? = 1 by…

A: Image is attached with detailed explanation.

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: I have solution for 1

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,yz) across the…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y²,z²)…

A: To apply the divergence theorem, calculate ∇·F, where F=x2,-y2,z2.…

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (-3x, y, 8z) across the…

A: Given:F=-3x,y,8zS=x,y,z:x2+y2+z2=6

Q: Use Green's Theorem to find the work done by the force field F(x,y)= (x3-x2y)i+xy2j   on a…

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Q: Use the Divergence Theorem tO compute the flux oT the field 1 25x cos z, 6xy ) out of the region E…

A: Given,       1z2+y2arc tanxz2+y2, 25xcosz, 6xy out of the region E that lies between the spheres…

Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (9xy², yz²,9zx²) through…

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Q: Find the circulation of the fieldF = (x2 - y)i + 4zj + rk around V? + y?, the curve C in which the…

A: Field F→=x2-y i^+4z j^+ x2 k^Surface S is cone z=x2+y2at plane z=22=x2+y2x2+y2=4So, f=x2+y2-4

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,y,z) across the…

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Q: Find the surface integral to evaluate the flux of the vector field F=, where S is the surface of the…

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Q: Use the Divergence Theorem to compute the flux of the field 1 cos (y)) out of the region E that lies…

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Q: Consider the closed, solid region E between the paraboloid z = 4 – x? – y? and the xy-plane, and…

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Q: Consider the vector field F = (x + y) i+ 2j + zk and the surface S defined as the surface of a cube…

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Q: Jse the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z) D is…

A: Given vector field is  F=x2,-y2,z2 D is the region in the first octant between the planes  z=4-x-y ,…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: According to the divergence theorem:

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, 3y, - 3z) across…

A: Let's find.

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Consider the vector field F = (x + y) i+ 2j + zk and the surface S defined as the surface of a cube…

A: Given vector is, F=x+yi+2j+zk From the Divergence theorem, ∬SF·nds=∭V∇·FdV

Q: Jse a CAS and the divergence theorem to compute the net outward flux for the vector field across the…

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Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Let C be the helix that winds around the cylinder x2+y? = 1 (counterclockwise viewed from the…

A: here i used parametric equation of helix and done simple calculation like dot product and after that…

Q: diverge

A: answer is in next step