If f(x, y) is a potential function for the gradient vector field F(x, y) (Зх — 2у) і — (2л — у) ј, — - - evaluate f(1, 2) – f(0, 1). 1. f(1, 2) – f(0, 1) : -3 2. f(1, 2) – f(0, 1) -1 - 5 3. f(1, 2) – f(0, 1) - 3 4. f(1, 2) – f(0, 1) = 2 - 5. f(1, 2) – f(0, 1) = -2

Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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

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Q: Find the work done by the force field F(x, y) =(2y'+2xy, 6xy+x +1) in moving a particle over the…

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Q: Find the gradient fields of g(x, y, z) = xy + yz + xz

A: Given that, g(x)=xy+yz+xz   We have to find, Gradient Field.   As we know,  grad…

Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

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

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Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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

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

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Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

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Q: 5. Let F be the gradient vector field of the function f (x, y) = 4xy + 3y". Evaluate JaF. dr, where…

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

A: It is required to find the conservative vector field for the potential function given in the…

Q: If F (x, y) = x2 i + y2 j is a conservative vector field, find its potential function. With the…

A: The solution are next step is

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: The conservative vector field: F = (2ry- z, r + 2z, 2y – 2rz). has potential function O 0 - 2y 212…

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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: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: Find the divergence of the vector field v = (x²y² - z3)i + 2xyz j + e*yzk. a) 2xy2 + 2xz + xy e*yz…

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Q: Find the gradient field of the function, g(x,y,z) = e 3z - In (x +2y).

A: Given function  gx,y,z=e3z-lnx2+2y2                     (1) The gradient field is  ∇g=∂g∂x,∂g∂y,∂g∂z…

Q: Find the gradient vector field of f(x, y, z) = x³y* + y° z³ + xz°.

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Q: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Find the gradient vector field of f(x, y) = tan(2x − 3y).

A: Given fx,y =tan2x-3y         we find the gradient vector of fx,y

Q: Find the gradient vector field of f(x,y) = In(x + 5y). 1 -i+ x + 5y 1. x + 5y 1 -i+ x + 5y 1 j x +…

A: We have to solve

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 work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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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: The gradient vector field of f(x,y)=y(2x2 -y3 ) is given by: O1. (2xy)i +(x2 -3y² »i O II. (4xy)i…

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Q: 2x Find the gradient vector field (F(, y, z)) of f(x, y, z) = y cos F(2,y, 2) =

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Q: Calculate the work done in moving a particle in the force field F = 3x2î+ (2xz-y)ĵ+ z k along a…

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Q: a) Determine whether or not the vector field F 8yz, – 6 cos(y) – 8xz, – 8xy + 10z > - is…

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Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) Ф(х, у) 3

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Q: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

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: Ğ(x, y, z) = (2z3 – 4y2 + Mxy, x2 - 8xy – Nz, 6xz? - My + 4) 1. Find the curl of G 2. Find M and N…

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Q: Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA,…

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Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If f(x,y)=x2+y², then the gradient field at (1,-1) is given by: O. f(x,y)= -2i + 2j O II. f(x,y)=…

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Q: 1. Is the vector field V (x, y, z) = (2ry, x² – 2², –2yz) conservative?

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Find the gradient vector field of f. f(x, y) = xe³xy Vf(x, y) =

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Q: Find a vector potential field for Ġ = [6xz+x³, –3r²y – y², 4.x + 2zy – 32²], i.e. find F such that V…

A: The solution is below.

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

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Q: (b) A potential function for the vector field F (x, y) = (2x + 1)(x² + x + 1)² 7+ (2y + 1)(y² + y +…

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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: If f(x,y) = x^3+y^3, sketch the gradient vector field: \grad{ f(x,y) }

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Q: 5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).

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Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.

Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…