Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for all constants c1, c2 € R and for all vector fields F, F : D → R³ that are differentiable. This property may be summarized by saying that the divergence is linear.

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

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Q: Find the divergence of the vector field F = ā x7, if r = xi+yj+ zk and ā = 3 i+3j+9k, by first…

A: First of all we calculated the vector F by calculating the vector product of the vectors a and r.

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: Find the divergence of the vector field.

A: To Find the divergence of the vector field.

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

Q: Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F…

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Q: Find the divergence of the vector field F. F(x, y) = 3xe*i - 9x²y²j

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Q: V.(V×F)= 0

A: Now given, ∇.∇×F=0 To prove the above.

Q: Let F be the vector field (ze"z + yz², xz², xeaz + 2xyz) (a) Find the divergence of F.

A: We will find out the required value.

Q: 3. Let F be the vector field (ze"z + yz², xz², xe™z + 2xyz) (a) Find the divergence of F.

A:

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 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 divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

A:

Q: Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

A: This question is belong to the vector calculus in which we have to deal with the divergence theorem…

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: 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: Let F be the vector field F(r, y, ) = =i- sin yj+ (2r: +6:)k. Compute divergence and gradient of the…

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Q: Use the divergence theorem to calculate the flux of the vector field F = x3i - 3x2yj + 6zk through…

A: The divergence theorem is defined by the formula, ϕ=∮∂VF·ndS=∮V∇·FdV Consider the given vector…

Q: Use Divergence Theorem to find the outward flux of field F = (-5x³ – 5y)i + (yz + 1)j + xyzk through…

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Q: Find the divergence in (2,1,-1) for the vector field FCX₁Y₁² ) = x³y² 2 ² + x ² z 3 + x^²yk

A:

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 = div F

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: Given the vector field F(7, y, 2) F (x, y, z) = compute the curl of F and find the values of a and…

A: curl(F)

Q: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

A: use divergence theorem

Q: Determine the divergence of these vector fields: (a) P = xʻyz a, + xz a, (b) Q3D p sin фа, + p'za,…

A: The given problem is to find the divergence of the given vector fields, We have to use Cartesian ,…

Q: Determine whether or not the vector field is conservative F(x,y) = 18x²y²i + 12x³yj conservative O…

A: NOTE: Refresh your page if you can't see any equations. . compare this vector field with  so here…

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: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: Use the divergence theorem to find the outward flux || (F-n)dS, where the vector field is given by…

A: Given that the vector field,

Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

A:

Q: What is the divergence of the vector field F of F(x,y) = x² i + 2y²j?2 div F = 2x + 4y div F = 4x +…

A: Given: F→=x2i+2y2j

Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)

A: We can solve this as follows:

Q: Calculate the divergence of the vector field F (x, y, z)

A:

Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: The divergence of the vector field F(z, y, z) = (ya°, az", zy?) is: %3D

A:

Q: Find the divergence of the vector field F div F =

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Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D…

A:

Q: (a) For any vector field F, the gradient of the divergence of F is always zero.

A: Since the gradient of divergence of F is given by

Q: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

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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: The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x²…

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Q: The vector field A=xa,+y² a, +=' a, is given. Verify the divergence theorem for this vector over a…

A: Use the Divergence Theorem we  find the outward flux of the vector field F = x2i+y2j+z2k across the…

Q: Determine whether the vector field F(x, y) = 5y2(yi + 2xj) conservative. F is conservative Fis not…

A: Just check if curl of F Is zero or not.

Q: If a vector field A(x,y,z)=xz3ex - 2x2yzey+2yz4ez , calculate the divergence ∇·A at point…

A: A vector field is given as  and

Q: Let F(x, y, z) = xyi + y²j, find divergence and curl of vector field F.

A: The divergence and the curl of a vector function, f(x,y,z) are defined as…

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

A: