Let vector fieldE =(3, y,x) across the surface S which is a cylinder x + y =9 with 0sz<3. 1) Sketch the surface S. 2) Evaluate [[ Fn dS .

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Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (ein z + 2y², 6x + tan¬1…

A: Given force field is F→(x,y,z)=esinx+2y2, 6x+tan-1y, xz Now, we will find the Curl(F→).…

Q: Consider the vector field Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j (a) compute the curl (b)…

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…

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Q: Evaluate the surface integral ∬SF⋅dS∬SF⋅dS for the given vector field FF and the oriented surface…

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Q: Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle…

A: According to the given information, it is required to calculate the work done by the force field

Q: Let vector field E =(y,z,x) across the surface S which is a cylinder x + y = 16 with 0<z<2 in first…

A: Surface integration

Q: Determine the work done by the force field F(x, y, z) = (x − y2, y −z2 , z − x2) on a particle that…

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Q: Verify Stokes Theorem for the vector field F(x, y, z) = (y-z)i + 3xy j + 5zk by evaluating the line…

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…

A: It is known that

Q: Verify Stokes' theorem for the vector field F(x, y, z) = zî + xj + yk taken over the half of the…

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Q: Apply fundamental theorem for conservative vector field to find the line integral fF dr where F =…

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Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

A: Let E be a three-dimensional solid bounded by a piecewise smooth closed surface S that has…

Q: Use Divergence Theorem to evaluate the flux integral ∫∫F·ndS, where F = 〈x^2, y^2, z^2〉, S is the…

A: Divergence theorem:∫∫sF.⇀  N^dS =∬∫DdivF⇀dV , here D is the solid bounded by the closed surface S.

Q: Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find…

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Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Let C be any smooth simple closed curve with positive orientation that lies entirely in a plane with…

A: Step:-1 Stock's Theorem:- ∫CF.dr=∬Scurl(F). ds=∬Scurl(F). n dA Part (a):- Given that F→=9y, 3x, 6z…

Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: A vector field is given as F = âr2r“ + a¿r²CoSo + âz5z. Verify Stokes theorem for this vector field…

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Q: Verify Stokes' theorem for the vector field F(x, y, z) = zî + xj+ yk taken over the half of the…

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Q: Define the force field ₹(x, y, z) =. Let S be the portion of the plane z = 2 - 2x in the first…

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Q: Use the divergence theorem to evaluate the surface integral F · dS, S where the vector field is F =…

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Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: Use Stokes' Theorem to find the circulation of the vector field F =7xzi+(4x+5yz)j +5x^2k around the…

A: F=7xzi+(4x+5yz)j+5x2k,andcircle : x2+y2=1,z=4

Q: Let S be the surface in the xy-plane defined by the inequalities |æ|+ |y| < 1, k. Verify the Stokes…

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Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…

A: Given To find the work done by the force field Fx,y,z=(y+z,x+z,x+y)  on a particle that moves along…

Q: Evaluate the surface integral Js F · dS for the given vector field F(x,y, z) = 7xi+ 4yj+7zk and the…

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Q: Compute the line integral of the vector field F=⟨6y,−6x⟩ over the circle x2+y2=1 oriented clockwise…

A: Given: F=6y dx - 6x dyand Let  x= cos t,   y= sin t    ⇒   dx = -sin…

Q: Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x2 - y2,…

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Q: Let vector field F=(y.z,x) across the surface S which is a cylinder x +y =16 with 0s:s2 in first…

A: The given problem is to sketch the given surface and also evaluate the double integral across the…

Q: Compute the line integral of the vector field F = (4y, –4r) over the circle z2 + y? = 16 oriented…

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Q: Use Green's theorem to find the work done by the force field F(x.y) %3D хyi + 1 x²+xy]j on a…

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Q: Show that the vector field F = 2.xyi + (x – 2 y)j is conservative and evaluate the line integral %3D…

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Q: . Verify Stoke's theorem for the vector field F = (2x - y) I– yz²J -y z K over the upper half…

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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: Verify Stokes' Theorem for the vector field F(x,y,z) = z^2i - 2xj + y^3k taking the surface S as the…

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Q: Verify Stokes' theorem for the vector field F(x, y, z) = zî + xj+ yk taken over the half of the…

A: According to the given information it is required to verify the stokes theorem for the given vector…

Q: (a) Set up a double integral for calculating the flux of the vector field F(x,y,z) = yi +5j − xzk…

A: Let r(x,z)=x,x2+z2,z Then the flux is given by, Flux=∬F.dS=∬F.(rx×rz)dxdz Here, rx=1,2x,0  ;…

Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y + z)k and the surface z = 4 – x²…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.

Q: Confirm that the force field F = xy'i+ x²yj is conservative in some open connected region containing…

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Q: Confirm that the force field F(c, y) = 2xy³i + 3x?y?j is conservative in some open connected region…

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Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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Q: Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface…

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Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (esin x + 2y², 6x + tan-…

A: We have to find the work done by the force field F→x,y,z=esinx+2y2,6x+tan-1y,xz in moving a particle…

Q: Let S be the part of the plane 2x + 5y + z = 4 which lies in the first octant, oriented upward. Find…

A: Given, S be the part of the plane                        2x+5y+z=4        which lies in the first…

Q: 4- Evaluate the surface integral of the vector field F = [ax, by, cz] over the sphere r² + y² + 2² =…

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Q: Let S be the part of the plane 2x + 2y + z = 4 which lies in the first octant, oriented upward. Use…

A: Given  plane  2x+2y+z=4

Q: Calculate the vector field flow f➝ (x,y,z) = (xy, y2, z) through the outer surface of solid T in the…

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