Let g, h: -R and /:R'+ R be defined by /(x, y) = (g(x, y), h(x, y). Assume curl /(x, y) = 7x – 7y, divf(x, y) = 7y – 8x, and Vg(x, y) = (2x – 4, 6y – 6x). Find the h(x,y) =( "(1,-1)%3D

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

A:

Q: Let S be the closed cylinder bounded by the surface r2 + 2² = 4, and the planes y = 1 and y = 4. Use…

A: Let's find.

Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 4+ x + 3y above the…

A: The surface integrals compute the flux of fields across surfaces,                   So,…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A:

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

Q: Compute the scalar line integral x – yz ds where C is the line seg- ment from (0, 1, 1) to (1,0, 1).

A: Given  ∫C x-yz   ds    where C is line segment from (0,1,1) to ( 1,0,1)

Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

A:

Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

A:

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

A:

Q: b) Show the force field M UTM UTM F(r, y, z) = (r²y + In(yz)) i+ UTM 3 + y cos(2z) ) j+ tial…

A:

Q: Compute the flux of the integral of the vector field F(z,y, 2) = (2,y, 2) through the half cylinder…

A: Given vector field is, Fx,y,z=x,y,z. It can be written as,  Fx,y,z=xi^+yj^+zk^. Flux of vector field…

Q: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…

A:

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

A:

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 / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Let S be the closed cylinder bounded by the surface x2 + z2 = 4, and the planes y =1 and y = 4. Use…

A:

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

A:

Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: (15) Find the divergence and curl of i = (ryz)î + (3x²y)ĵ + (æz² – y²z)& at point (2, –1,1).

A: Given v→=xyzi^+3x2yj^+xz2−y2k^ We have to find the divergence and curl of v→ at point 2,−1,1. If…

Q: Compute the line integral of the vector field F = (3zy1, 4z, -y) over the path c(t) = (e*, e', t)…

A:

Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

A:

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

A:

Q: Show that the vector field F = 2xyi + (x² – 2 y)j is conservative and evaluate the line integral…

A:

Q: Show that the vector field F=2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

A:

Q: 2的 在年

A:

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(x + 3y + 4z) . F(2, y, 2) =

A:

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 <y<9, x…

A:

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

A:

Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

A:

Q: For the vector Ā =e - yzē, + xzē, and scalar function f(x,y, z) = x² sin(y) + y a) Obtain the…

A:

Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…

A: Given, the velocity field v→=0, y, 0and S be the surface defined by y=x2+z2, with y≤1.

Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

A:

Q: Find the flux out of the curve bounded by the top half of = arccos(√√²+² ) and y=0 with vector field…

A: As per the question we are given a bounded curve C and a 2d vector field F And we have to find the…

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: If F = xy i+ (x² + 4yz)j+ 2y²z k. Evaluate the line integral between A (0, 2, 0) and B (3, 6, 1).…

A: Given, F= xy i +(x²+4yz)j +2y²zk r0= (0,2,0) r1= (3,6,1)

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) 5zy ze F(1, Y, 2) =

A: Gradient vector field F→(x,y,z) of a function f(x,y,z) is given by,…

Q: Let F(x, y, z) = (8 + 8y+ 3z+yz, 6x + 6y + 2z+ cz, 5x + 4y+ 10z+ ry). and let C be the curve that…

A:

Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

A:

Q: Verify Stokes' Theorum for F(x,y,z) = (y,-x,yz) if S is the paraboloid z = x2 + y2 with x2 + y2 = 1,…

A: Given  Fx,y,z=y,-x,yz Then, F→=yi^-xj^+yzk^

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = z sin(ry). F(2, y, z) = (

A: Given function is  f(x,y,z) = z^2 sin(xy)

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…

A:

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = x² sin(3yz) F(z, y, 2) = (

A:

Q: Let - (xz, 5 - 4xyz, xz) be the velocity field of a fluid. Compute the flux of i across the surface…

A:

Q: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 &lt;= z &lt;= 2

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

A:

Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

A: