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Does the function f(x,y)=x2+y2 satisfy the two dimensional Laplace's equation? Explain why/why not And then calculate...

Does the function f(x,y)=x2+y2 satisfy the two dimensional Laplace's equation? Explain why/why not

And then calculate the gradient of g(x,y) at points g(x,y)=(0,1), (1,0), (0,-1) and (-1,0) and indicate by little arrows the directions in which these gradient vectors point.

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