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

Q: The gradient vector field of for,y)= In +2y) is 2. T True A False

A: The gradient vector field of a function, is defined by the formula below. , where are the partial…

Q: Find the divergence of the vector field F <7", 22°, zy* div F -

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Q: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: Find the divergence of the vector field F = < yx®, xy®

A: Given,         The vector field is F¯=&lt;yx3 , xy6&gt; .

Q: Find the divergence of the vector field F(x,y,z) = (ye*,2x + 3y, ycosx).

A: Consider a vector field is defined as, Fx,y,z=f,g,h The divergence of the vector field is defined…

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

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: 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: Match the vector field with its graph. F(x, y) = yi -6+

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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: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Find the curl and divergence of the vector field. F(x,y,z)=x^2yz i -x x^3y k

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

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Q: xi + yj x2 + y2' F(x, y) = k

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Q: Find the work W done by the vector field ⟨2x+yx,x2+4⟩ on a particle moving along the boundary of the…

A: To find the workdone by the vector field.

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 of the vector field F F(x, y, z) = In(x² + y²) i + xy j + In(y² + z²) k

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Q: Calculate the divergence of the scalar field F(x,y)=3x2+siny.

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Q: Find the divergence of the vector field F. F(x, y, x) = i+ zj - 8y²zk %3D O2+ 7- 8y O zi+ 7zj - 8y²k…

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Q: Find the divergence of the vector field F div F -6z sin (a + 7) %3D

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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 divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

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

A: The solution is:

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: 1 Find the divergence of the vector field F -(xi + yj+ zk) Vx? +y? +Z 2 x² + y² + z? 1 x² + y? + z?…

A: If the vector field is given by F=F1i+F2j+F3k then the divergence of F is ∇·F=∂F1∂x+∂F2∂y+∂F3∂z.

Q: Determine if F = (12r – 2x cos y, 2y + x² sin y) is a conservative vector field. If it is, find a…

A: Given that F=(12x3-2xcosy)i+(2y+x2siny)j. We need to determine whether if F is conservative field or…

Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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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: Find the gradient vector field ∇f of f(x, y) = x2 − 4y.

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Q: Find the divergence of the vector field F(x, y, z) = In(x² + y? )i+xyj+ln(y² + 2²)k. 2x 2z +x + x2 +…

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Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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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 = < yx², xz", zy® div F II

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Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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

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Q: Compute the curl of the vector field F = 2y3 i+ e j+ cos(x) k curl

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Q: Compute the flux of the vector field F = 2xi + yj through the cylindrical 5 and b = 4 and it is…

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Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

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

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Q: Consider the conservative vector field given by: F (x, y) = (x - ycos (x), y - sin (x)) A potential…

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Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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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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