Consider the function G(z) = z¹/². a) Find the regions of analicity of G(z) b) Derive a conservative field associated to the potential function (p = Re G(z).

Q: 2) Let F= 2 xyi + (x² + 2) j. find a potential function, f, for it. Show that Fis conservative and

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Q: Determine whether the vector field F(x, y) = 4 sin(y)i + (-8y + 4x cos(y)) is conservative or not.…

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Q: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

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Q: a) Calculate the line integral of the vector field F(x, y) = yi − 5xj from the point (0, 3) to the…

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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: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

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Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

Q: ) Let F(x, y) = (3x² + y²)i + 2xyj. (a) Test if F is a conservative vector field. (b) If F is…

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Q: y +3z x + 2z 2y + 3x Consider the conservative vector field F(x, y, z) = with domain R³. Find a…

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Q: Consider the vector field F (xr, y) = (2y - 12r*y", 4ry – 9r*y?) is conservative. (a) Show that F…

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Q: 2. Find the gradient field F = Vy for the potential function p. Sketch a few level curves of o and a…

A: Given φ(x,y)=2x2+4y2 The gradient field  F=∇·φ=∂φ∂x,∂φ∂y=4x,8y Some vectors of F are  At x=1 and y=1…