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

Q: Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: Find the gradient vector field of f.  f(x, y, z) = 8sqrt(x^2 + y^2 + z^2).

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Q: Find the work done by vector field F(x, y, z) = xi + 9xyj - (x + z)k on a particle moving along a…

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Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = x°y*2? . F(1, Y, 2) =

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Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

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: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(6r + 2y + 2) . F(2, y, 2) =

A: Find the gradient vector field

Q: Find the gradient vector field of the function f. f(x, у, 2) 3 3x соs Vf(x, у, 2) %3D

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

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Q: ..Find the Gradient Vector Field for: f (x,y, z) = x²ye/z

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Q: Find the gradient vector field of f(x, y) ,3

A: Given,          The gradient vector field of fx,y=x6y3.

Q: Find the conservative vector field for the potential function by finding its gradient. (x, у, 2) %3…

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Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Find the conservative vector field for the potential function by finding its F(x, y) = x² + 5y2

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Q: Find the flux of the vector field F = (x, z, - y) through the helicoid with parameterization r(u, v)…

A: Given :-  The flux of the vector field  F→ =  x3 , z , -y through the helicoid with the…

Q: Determine if the vector field F=(yz,xz,xy) is conservative?

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Q: Find the gradient vector field of the function f. f(x, y, z) = 6ze-xy Vf(x, y, z) =

A: To find the gradient vector field of the given function f.

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y) = x²…

A: Here we have to use the concept of gradient

Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, у, 2)…

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Q: Explain why the vector field ∇(xy + xz - yz) is conservative.

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

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Q: Find the gradient vector field of f(x, y) = x°y*

A: Given,          The gradient vector field of fx,y=x5y4.We know that,          The gradient vector…

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

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =

A: we have to find the gradient vector field of f

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: Find a potential functioon for the conservative vector field given by y3/2 3 xy + z, 2 sin z 2.x…

A: According to question,Given vector field,F→x, y, z = 2xx2 + cos z-y322x, -32xy+z, -sin zx2 + cos z+y

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

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Q: Find the gradient vector field (F(x, y, z)) of f(z, y, z) = e®2z + $y + 2= F(1, y, z) =

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Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

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

A: Given: f(x, y, z) = 9x2 − xy − z2

Q: Find the conservative vector field for the potential function h(x,y,z) = 16xy ln(x+y) by finding its…

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Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

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Q: Determine the gradient of the give scalar field V = e(2*+3y) cos 5z at R(-0.1, 0.2, 0.4).

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

A: The gradient of a function is the rate of change of a function and for a function, f(x,y,z), the…

Q: Find the gradient vector field of f(x, y) = x° sin(9y). F(x, y) = x°i+ sin(9y)j F(x, y) = 9x°…

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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: Find the conservative vector field for the potential function by finding its gradient. g(r, y, :) +

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Q: Select the irrotational vector field. OAyz 1-2xz1 + xyz k OB. yz 7 + xz 7 + xz R OCZ7 + z? Î + yz R…

A: We will find out the required value.

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

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Q: Suppose a vector field F(r, y) = construct a potential function o(r, y). i+ j is conservative. Then

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

A: We have to find the conservative vector field.

Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: Compute the outward flux of the vector field F = (5xy, 5y²) for the region enclosed by the curves y…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: 5sqrt(x^2 + y^2).

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

A: We have to find the conservative vector field.

Q: Find the gradient vector field of f(x, y, z) = e9z+6y+7z V

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