Show the each of the vector fields F rightarrow = 5y i rightarrow + 5x j rightar

Question

Show the each of the vector fields F rightarrow = 5y i rightarrow + 5x j rightarrow , G rightarrow = 5y / x2+y2 i rightarrow + -5x / x2+y2 j rightarrow , and H rightarrow = i rightarrow + j rightarrow are gradient vector fields on some domain (not necessarily the whole plane) by finding a potential function for each. For F rightarrow, a potential function is f(x, y) = For G rightarrow, a potential function is g(x, y) = For H rightarrow, a potential function is h(x, y) = Find the line integrals of F rightarrow, G rightarrow, H rightarrow around the curve C given to be the unit circle in the xy-plane, centered at the origin, and traversed counterclockwise. F rightarrow . dr rightarrow = G rightarrow . dr rightarrow = H rightarrow . dr rightarrow = For which of the three vector fields can Green's Theorem be used to calculate the line integral in part (b)? It any be used for (Be sure that you are able to explain why or why not.)

Explanation / Answer

greens. theorem can be used in b part

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