Examine the behavior of f (x, y) = x4 y4/(x2 + y4)3 as (x, y) approaches (0, 0) along various straight lines. From your observations, what might you conjecture lim(x,y)→(0,0) f (x, y) to be? Next, consider what happens when (x, y) approaches (0, 0) along the curve x = y2. Does lim(x,y)→(0,0) f (x, y) exist? Why or why not?
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