The vector field A=xa,+y² a, +=' a, is given. Verify the divergence theorem for this vector over a cube 1 m on the side. Assume the cube occupies the space 0 Sr, y, :<1.

Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

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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: Sketch the following gradient vector field, F(x, y, z) = 2xi - 2yj – 2xk. Then find the vector…

A: The given problem is to sketch the given vector field and also to find the gradient of the given…

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: When is the vector field continuous?

A: given,       Continuous vector field .

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = −1xyi – 2yzj —…

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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: Compute the flux of the vector field F 3.ri + 3yj through the cylindrice surface shown below, if a=3…

A: To calculate the flux of the vector field.

Q: A vector field is described as F = (-z + 7x, x³y²z=1,3x + 2z²). (i) Calculate curl F. (ii) Determine…

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Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: Let F = (0, x), a 2D vector field. Compute fF . T ds, where C is the top half of the circle of…

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Q: Compute the flux, || Foñds, across the slanted face of the tetrahedron 2 = 4-1- y bounded in the…

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Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

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Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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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: Determine if the vector field F(x,y)= (x+y,x−y) is conservative? If it is, find its potential.

A: Given Data The vector field is: F(x,y)=(x+y,x-y).   Write the vector field in standard form, The…

Q: Show that the vector field F = 2xyi + (x - 2 y)j is conservative and evaluate the line integral %3D…

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Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

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: Write a formula for a two-dimensional vector field which has all vectors of length 1 and is…

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Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2j+ Cx tk, %3D where the coefficients A,…

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Q: Explain why the vector field ∇(xy + xz - yz) is conservative.

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Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

Q: Consider the vector fields A given by: A(r,0,4) = r sin0 cospx+r sin0 sinoŷ+r cos0î. Verify the…

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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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: Write a formula for a two-dimensional vector field which has all vectors of length 7 and…

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

A: Let the given vector field is :

Q: Determine if the vector field is conservative. 1 -) (yi + «j) F(x,y) = 1+ xy, conservative not…

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Q: Find the divergence of the given vector field at point (1,1,1). Insert your answer below. Round to…

A: Fx, y, z=3x2yi+2xz3j+y4k Comparing with F=Pi+Qj+Rk, we get P=3x2y,  Q=2xz3,  R=y4 Now, ∂P∂x=∂3x2y∂x,…

Q: b) Find the curl of the vector field, CurlF, if F = Ax²z²i– By:'j+Cz*k, where the coefficients A,…

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

Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: What is the divergence of a vector field? How can you interpret it?

A: Divergence of a vector field:

Q: Find the curl and the divergence of the vector field. F(x, y, z) = x²yzi - x³y k i + Submit Answer…

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

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Q: Find (a) the curl and (b) the divergence of the vector field.

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Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path:…

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Q: Find the curl and divergence for the given vector field.

A: →Divergence is a measure of spread of vector field at a point.→Curl describes the infinitesimal…

Q: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

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Q: Calculate the divergence and the curi of the following vector field at the point (1. 2. 1) Fix, y,…

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Q: Find a vector field with twice-differentiable components whose curl is x i + yj + z k or prove that…

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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: 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: Give an example of a vector field F (x, y, z) that has value 0 on precisely one line and such that…

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Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

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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: : Verify the divergence theorem for A=4xi +(2Y+z Vector field ) | +(52-2x)k in the regim beunded by…

A: According to the given information, it is required to verify the divergence theorem for a vector…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.