If C is the curve given by r (t) = (1+2 sint)i+ (1+ 2 sin? t)j+ (1+1 sin' t) k, 0

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: Consider the force field F = (2xzez — 4, cos³ z, x²eª²z – 3y cos² z sin z Find the work done by F in…

A: Given: The force field is F→=2xzex2z-4,cos3z,x2ex2z-3ycos2zsinz and the given given curve is…

Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

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: 4. Is this vector field F(x,y)=(ycos x)ĩ +(sin x+ y)j being the path-independent field? Please show.

A: To check if the given vector field is path-independent field or not. Given:

Q: Find the conservative vector field for the potential function by finding its gradient.

A: Gradient for function h is given by , where are the partial derivatives. Partial derivative…

Q: Find the curl of the vector field F (5x sin(y), 2y cos(æ)) curl F =

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Q: Find the total work done in moving particle in a free field given by F = 3xyi – 5zj + 10xk along the…

A: The total work done by a vector field, F→ moving a particle along the curve r→(t) is calculated…

Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

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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: Find the work done by the vector field f = to move a particle along the arc of the hyperbola y=1/x…

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Q: Confirm that the force field F = xy²i + x²yj is conservative in some open connected region…

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Q: Compute the flux SS F.nds through the piece of the cylinder of radius 2, centered on the z-axis,…

A: The given surface is the cylinder of radius 2 centered on z-axis, where 0≤x, 0≤y and 0≤z≤4. The…

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 flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

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Q: 5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential…

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Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: Evaluate line integral of vector field F(z,9) = i+ 1- x? y2 2x along the curve x = cos(t), y =…

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Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

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

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Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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

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Q: If the components of a vector field F have continuous second partial derivatives and S is the…

A: Given that The surface S is simple and F is twice differentiable To show ∫∫scurlF.ds=0

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: 2的 在年

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Q: Consider I = ∫CF⋅dr, where (img17) is a conservative vector field and curve C is parameterized by:…

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Q: Find the curl of the vector field F = (6y cos(x), 7x sin(y)) curl F =

A: If  F=f1x,y, f2x,y   thenCurl F=0,0,∂f2∂x-∂f1∂y

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

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: Calculate the work done in moving a particle in the force field F = 3x2î+ (2xz-y)ĵ+ z k along a…

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Q: Without using a potential function, find the total work performed by the force field F(x, y) =…

A: The work done by the path E is given by, W=∫EF.dr If the force vector is: F(x,y)=&lt;2xsiny+y2ex,…

Q: Consider the vector field F (x, y, z) = (2e2" cos(3y), –3e2" sin(3y) +VV?) Y y' 2 COS a. Find…

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Q: Compute the work done by the force field F = , 0 <t<1

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Q: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: The movement of air on the surface of a certain closed controlled space is studied, and every point…

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Q: Suppose you need to integrate the vector field v = (3 cos z, e+, sin(y)) along the curve…

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Q: Let W be the region between the sphere of radius 4 and the cube of side 1, both centered at the…

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Q: A=(2x-3y)ax+(2xy-y2)ay Prove the Stokes theorem for the triangular linear path in the shape that is…

A: The general form of a vector valued function in a plane is given by A=Axax+Ayay, where Ax and Ay are…

Q: 6. Compute ſ, F-·dr where f(x, y) = (y² cos x, 2y sin r) and C is the straight line path starting at…

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Q: Without using a potential function, find the total work performed by the force field F(x, y) = (2x…

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

A: Application of integral: The force acting on the particle, F⃗ =4yi+2xj  Let the particle undergo a…

Q: he line integral of the vector field F= over the curve C which is the quarter of the rcle from…

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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: The integral of the vector field F(x, y) = (cos |x|, sin y|) A = (-2,0) and final point B (0, 2),…

A: Correct answer is (B) sin(2) - cos(2) + 1 Explanation:

Q: Consider the vector of electric field Е(х, у.2) %3 (sinh x)1 - (сosh y)) — хуг k a. Compute the…

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Q: Compute the divergence and curl of the vector field cos (22 ) sin² (z² yz) 10 yz4 – xyz2 at the…

A: We have to find divergence and curl of vector field:

Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical…

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