The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz - k. Find div F at (1,0,0) and determine whether F is conservative without looking for a z²+1 potential function.

Q: The potential of the conservative vector field F = (y,x,1> is Of=z+xy O f=x+yz O f=y+xz Of = xyz

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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 outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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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 work done by vector field F(x, y, z) = xi + yj + (x + z)k on a particle moving along a line…

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Q: Consider the vector field F(x, y,z)= 2.xy i+(x² +z² ) j+2yzk. c) Is F a conservative vector field?…

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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: For the vector field F(x, y, z) = (15x2y + 2xz)i + (5x3 + 35y4)j + x2k, show that F is conservative…

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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: If a vector function v(t) = (t, Int,t-²) is given for a scalar function Ø = x In z + Jy - cos(x + 1)…

A: Given the scalar function φ=xlnz+y-cosx+1. This scalar field is to be evaluated over the path…

Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe² – y²sin x)î +…

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Q: Find the flux of F = yi + 2zxj – z²k through the parabolic cylinder y = x2,0 < x < 1,0 < z< 4, in…

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

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

A: Given:

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 gradient vector field of f(x, y, z) = e3r + 8y+6z

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Q: Show that the vector field F = x²i + (2yz)j+ y² k is conservative and then find the corresponding…

A: A vector field F is conservative if curl(F)=0 or ∇×F=0 The potential function is given by f such…

Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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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: It is known that

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 F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: The vector field F (x,y) = (sec²x, 3y²) is conservative. Find f(x,y) such that F = Vf. f= ytanx + xy…

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

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Q: Q3) Determine if the vector field F(x, y, z) = (yz,xz + 2y, xy + 1) is conservative. If it is, find…

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

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Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

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Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: Evaluate the outward flux of the vector field F = (2x? – 5e" + sin(2²), –4ry + ln(x*), 5z – 3x²y°)…

A: Given

Q: The vector field F = (, i, 2²) has a scalar potential in the region R= {(x, y, 2) E R³ : r² + y? >…

A: We find out true or false.

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 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: Find all potential functions of the conservative vector field F (x, y, z) = (2xz + y², 2xy,x² + %3D…

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

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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: The vector field F = ( z, z²) has a scalar potential in the region R = {(x, y, z) E R° : x² + y? >…

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Q: (a) Show that the vector field F(x, y, z) = (1 + 3x²y)i + x³j is conservative and find the potential…

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

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

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

A: Given the vector field

Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

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

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Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: Find the gradient vector field of f(x, y, z) = e® 5x+2y+8z

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Q: Show that the vector field F(x,y,z)=yz^2i+xz^2j+2xyzk is conservative, find a potential function f,…

A: The given vector function is F(x,y,z)=yz2i+xz2j+2xyzk The given vector field F is conservative if…

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: 3. Determine if the vector field F(x, y, z) = e" sin yzi + ze² cos yzj + ye² cos yzk is conservative…

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Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe? – y²sin x)î +…

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