Calculate the flow/line integral in the field F along the path C. F = (x - y) i - (x2+y 2) j; C is curve from (2, 0) to (-2, 0) on the upper half of the circle x2 + y 2 = 4 O 47 - 1 4 - 2TT 4TT

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Q: find the curl of U = exy ax +sin(xy)ay + cos2(xz) az

A: U=exyax+sinxyay+cos2xzaz

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:

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Q: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

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Q: = (4x° – 7y)i + (9y' + 7x – 7)j %3D - ndary of the parallelogram in the following figure (note the…

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Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

A: Given F→=y,x+2y We have to find the ∫CF→⋅dr along the given path.

Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: late the F= (x - y) i - (x 2 + y 2) j; C is curve from (4, 0) to (-4, 0) on the upper half of the…

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Q: The gradient of f (x, y) = x sin (y²) is the vector field F(x, y) = at (2,√7/6) and ending at…

A: The given scalar function is, f(x,y)=xsiny2. Gradient of this function is F=siny22xycosy2. The…

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Q: Sketch the slope field for the points (ti, y;) where at and dy dt y-2 Z₁ = -1 + 0.25(1-1) = for…

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Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What…

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Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: Show that the vector field F(x, y, z) = (-4y cos(4x), 4x sin(–4y), 0) is not a gradient vector field…

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Q: Ex: Find the work done by the vector field F = (y-x²)i + (z - y²)j + (x-z²2)k Over the curve r(t) =…

A: Given: F=y-x2i+z-y2j+x-z2krt=ti+t2j+t3k

Q: The circle of radius a centered at the origin, and the vector field F = -i + yj.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

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Q: (a) Consider the vector field G = (xyz, yz, xz). Find div(G). (b) (1,2,3). Using the G from part…

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Q: 3. Consider the vector field F(x, y) = (3y²+ 4x, 5y sin(x)). (a) Calculate curl F at the point (0,…

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Q: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

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