Suppose F(x, y) = (2 + 5y, 6z – 5y²). Use Green's Theorem to calculate the circulation of F around the perimeter of the triangle C oriented counter-clockwise with vertices (10,0), (0, 5), and (-10,0). F- dř =

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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 work done by the force field F(x,y) = 4yi + 2xj in moving a particle along a circle x2 + y2…

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Q: If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2.…

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Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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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: If F = xi + -4yj +x2k determine the flux of F through S, where S is the portion of z2 = x2 + y2,…

A: Given - F = x i^ - 4y j^ + x2 k^  ;             S is the portion of z2 = x2 +y2 , 1 ≤ z ≤ 3 To find…

Q: Use Stokes's Theorem to evaluate F(x, y, z) = x²i + z²j – xyzk S: z = √√√4x² - y² F. dr. In this…

A: Consider the given function, Fx,y,z=x2i+z2j-xyzk and S:z=4-x2-y2 Let us consider that ϕ:x2+y2+z2=4.…

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

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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: Let flxiy) = Rx Jy 27 %3D a) Finid the gradrent of f b) Find the directional derivative of f at the…

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A: Consider the given function. The divergence theorem is defined as. Now, find the value of div F.

Q: rotational velocity field v = ⟨0, 10z, -10y⟩ . If a paddle wheel is placed in the plane x + y + z =…

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Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

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

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Q: find the outward flux of F across the boundary of D.  F = 2xyi + 2yzj + 2xzk D: The cube cut from…

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

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Q: Let F = (2z, - x, 3y): Find the flux of F, that is, - dS, where S is the graph of the function z =…

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Q: Consider the force field F = (ev – e2" , (x + })ev) and the curve C = C¡U C2 where Cı is the line…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

Q: Find F.dS if F (x, y, z) = 2xi+2yj+2zk and S is t he part of the paraboloid z = 8-x²–-y? lying above…

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Q: Use the Divergence Theorem to find the flux of F = (xy², x²y, y) outward through

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Q: Find the circulation of F over the counterclockwise closed curve C: F= tan-1yi+ + 2x + y+z)j +yk…

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Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

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Q: Compute the flux ∮∂D F • n ds of F(x, y) = {x3, yx2) across the unit square D using the Flux Form of…

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Q: For the vector Ā =e - yzē, + xzē, and scalar function f(x,y, z) = x² sin(y) + y a) Obtain the…

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Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

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Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…

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Q: For a certain fluid flow field the velocity is given by V = [y² – x(1+ x)]i+ [y(2x + 1)]j+k. Show…

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Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

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Q: Let f = (r +2ryz)i+( + 2xy)j+ (+ 2xyz)k. Find j at (1.0, 1). (a) divergence of

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Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

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Q: H.W: Select the divergence of F(x, y) i+ (2x – 3y)j. %3D 1 (b) -* +2, y2 1 (c) (a) 3, (d) -2. - - -

A: Multiple:   Divergence of a vector field find by taking the scalar product of the vector operator  ∇…

Q: Find the work done by the force field F(x,y) = 4yi + 2xj is moving a particle along a circle x2 + y2…

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Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

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Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? 0. Then § (-2ydx + 3xdy) = a)…

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Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: If f(x,y) = x^3+y^3, sketch the gradient vector field: \grad{ f(x,y) }

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Q: Let if (x, y, z) # (0,0, 0) if (x, y, z) = (0, 0, 0) xyz x²+y²+z² > f(x, y, z) = { 10, (a) Use the…

A: fx, y , z = xyzx2 + y2 + z2, if (x, y , z) ≠(0,0,0)                             0,…