Calculate the divergence of the vector field. F(x, y) = 3x°i – 2x sin(xy)j div(F) =

Q: Find the divergence of the vector field.

A: To Find the divergence of the vector field.

Q: Match the vector field with its graph. F(x, y) = xi + 3yj + +x ' ||||||||||| 畫 至 X

A: Solution is given below:

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

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

A:

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

A: Solve for the gradient vector

Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: Find a potential function for the vector field F(x, y) = (14xy + 7y- 8, 7z + 7z). f(x, y) =

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Q: Suppose the vector field F = yi + (x + Z)j + (y + 2z)k is conservative. Find a potential function of…

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Q: Find the conservative vector field for the potential function h(x,y,z)=3xyln(x+y) by finding its…

A: Find gradient

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

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: Find the divergence of the vector field F. F(x, y) = 3x2i + 5y?j %3D

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Q: Find the divergence and the curl of the vector field F(x, y, z) = x²yi + 2y'zj+3zk

A: The vector field given is : F(x,y,z) = x2y i +2y3z j + 3z k

Q: A conservative vector field is given as F = 6xe'i + (3x²e' –10yz')j-15y 2 k. Find the potential…

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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: Determine whether the vector field h(x,y) = y^2i + (2xy-e^2y)j is conservative or not. If it is…

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

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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: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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

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Q: (a) Is the vector field | F(x,y) = (xe, ye²) conservative? Justify your answer. If it is…

A: Let the vector field F = Pi + Qj.The above vector field is conservative if and only if dPdy=dQdx

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

A:

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 divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i – 3x?y?j

A:

Q: Find the divergence of the vector field F = < yx², xzª, zy³ div F =

A: f = y x2  ∂f/ ∂x = 2xy   g = x z4  ∂g/ ∂y = 0   h = z y3  ∂h/ ∂z = y3

Q: Find the divergence of the vector field F. F(x, y) = 7xe*i - 4x²y²j

A:

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

A:

Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

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

A: we have to find potential function.

Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

A:

Q: Graph the vector field F(x, y)=(-3y, 2x); also find the divergence and the rotational.

A: The graph of the  vector field F=-3y, 2x is as follows

Q: Find the divergence and the curl of the vector field .F(x, y, z) = 1 (xi + yj + zk).

A: F(x,y,z) =xi +yj+zkx2+y2+z2 it can be written as F(x,y,z) =xi +yj+zkr   where r =x2+y2+z2 divergence…

Q: Given a scalar function V(x, y) =-(x² +y² ), the directional derivative of V in the direction of the…

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Q: Find the gradient vector field of f(x, y) = ln(4x + 2y)

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Q: Find the curl of the vector field F = (3x sin(y), 7y cos(x)).

A: The solution is:

Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. 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) = 9x2 − xy − z2

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

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Q: Find the divergence at (15, 0, 0) for the vector field F(x, y, z)= e*sinyi-e cosyj+z²k O 16 O 451 30…

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Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 5x2y²j

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Q: Find the divergence of the vector field V(x, y, z) = -2e*'i – e³xyj+ 7e%yzk.

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Q: Find the divergence of the vector field V(x, y, z) = -2xi + (y + 5 cos(x))j+ (7z + e8xy) k.

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Q: Find the divergence of the vector field F. F(x, y) = 3x?i + 4y²j

A:

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

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Q: Find the conservative vector field for the given potential function. f(x, y) = 9x2 + 2xy + 10y2 F(x,…

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