Determine (a) whether f(x, y) is continuous at (0,0); (b) whether fx (0,0) and fy (0,0)...

  

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Determine (a) whether f(x, y) is continuous at (0,0); (b) whether fx (0,0) and fy (0,0) exist, and their values, if they do; (c) whether f(x, y) is differentiable at the point (0,0). (In each part, write your answer in detail!) (x²-y² Given f(x, y) = {x²+y²¹ 0, (x, y) = (0,0) (x, y) = (0,0) Determine (a) whether f(x, y) is continuous at (0,0); (b) whether fx (0,0) and fy (0,0) exist, and their values, if they do; (c) whether f(x, y) is differentiable at the point (0,0). (In each part, write your answer in detail!) (x²-y² Given f(x, y) = {x²+y²¹ 0, (x, y) = (0,0) (x, y) = (0,0)