Use a graphing utility to make a table showing the values of (x, y) at the given

Use a graphing utility to make a table showing the values of ƒ(x, y) at the given points for each path. Use the result to make a conjecture about the limit of ƒ(x, y) as (x, y) → (0, 0). Determine analytically whether the limit exists and discuss the continuity of the function.

 

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f(x, y) = Path: y = 2x - y² 2x² + y = 0 Points: (1, 0), (0.25, 0), (0.01, 0), (0.001, 0), (0.000001, 0) Path: y = x Points: (1, 1), (0.25, 0.25), (0.01, 0.01), (0.001, 0.001), (0.0001, 0.0001) -3-2 2 3