2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector field F(x, y) = (P(x, y), Q(x, y)) satisfying each of the following cases. Explain your answer in detail. (a) Qx(x, y), and F is a gradient (conser- (b) V(x, y) = D, Py(x, y) vative) vector field. V(x, y) = D, Py(x, y) (conservative) vector field. = Qx(x, y), and F is not a gradient

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A: on solving this we get the

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A:

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Q: 1. For each of the following vector fields F(1, y), decide if there is function f(z, y) such that F…

A:

Q: Consider the vector field F(x, y, z)  =  (Sx3y3z7)i + (3x4y2z7)j + (Tx4y3z6)k Find the values of S…

A:

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: Using arrows, clearly sketch the vector field u(r) = (y², x + y, 0) in the (x, y)-plane.

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A: solution

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