Use a table of numerical values of f(x, y) for (x, y) near the origin to make a conjecture about the value of the limit of f(x, y) as (x, y) → (0,0) . (if the limit does not seem to exist, enter dne.) f(x, y) = x y x2 + 2 y2

Seems to be that the limit to compute is



Consider an arbitrary line through the origin , so that we rewrite the above as



The value of the limit then depends on the slope of the line chosen, which means the limit is path-dependent and thus does not exist.

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