Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed cylinder of radius 4, centered on the y-axis, with -5 < y < 5, and oriented outward. flux =

Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

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Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: 1) Find the work done by the vector field F(x, y, z) = (x², 4xy³, xy²) on a particle that %3D…

A: Given force is F→x,y,z=x2,4xy3,xy2 Let r→=rt→ be the boundary of the rectangle with vertices  0,0,0,…

Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Find curl(curlF→(x,y,z)) of the vector field F→(x,y,z)=x^9zi→−9x^8zj→+yzk→. Enter the exact answer.…

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

A: We compute the flux of the vector field through the surface.

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: Use properties of the linear transformation T(x, y) = (3x − 2y, x + y) to determine if the matrix…

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Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

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Q: Verify the Divergence Theorem for the vector field F = (-2, 3, z³) on the sphere x² + y² +2²2² = 4…

A: For the vector functionto verify the divergence theorem over the sphere

Q: Find the curl of the vector field F = <yx³, xz³, zy² curl F = i + k + V

A: For the given field F=yx5, xz3, zy2, we need to calculate the curl. This can be evaluated as…

Q: Compute the curl of the following vector field. 4r (4x, 4y, 4z) 7/2 (4x +4y +4z) " 2r The curl of F…

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Q: nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of…

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Q: Compute the flux of the vector field (ï³, — xy³), out of the rectangle with vertices (0,0), (4,0),…

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

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Q: (b) If F(x, y) = (4x + 4y)i + (4x + 4y)j, then f(x, y) =

A: (b) The given vector field is  F→(x,y)=(4x+4y) i+(4x+4y) j. To Prove/disprove: The vector field is…

Q: Compute the flux of the vector field (4, - y²), out of the rectangle with vertices (0,0), (2,0),…

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Q: Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at…

A: Given,                    To find the flux of the given vector field through a disk of radius 6…

Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work…

A: Given point (2,4)  and (3,9)now equationof line passing through two point is given by…