Let f R2 R be defined by f(x, y) = xy2 x + y for (x,...

 

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Let f R2 R be defined by f(x, y) = xy2 x + y for (x, y) + (0,0). By considering appropriate curves that approach the origin, or otherwise, prove that there is no choice for f(0,0) that makes f continuous at (0,0). Let f R2 R be defined by f(x, y) = xy2 x + y for (x, y) + (0,0). By considering appropriate curves that approach the origin, or otherwise, prove that there is no choice for f(0,0) that makes f continuous at (0,0).