Use a graphing utility to make a table showing the values of (x, y) at the given points for each path. Use the result to

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.

 

f(x, y) = Path: x - Path: x = y Points: (1, 1), (0.25, 0.5), (0.01, 0.1), xy x + y4 = (0.0001, 0.01), (0.000001, 0.001) - y Points: (1, 1), (-0.25, 0.5), (-0.01, 0.1), (-0.0001, 0.01), (-0.000001, 0.001) 2 N y