Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of f(x, y) as (x,y) → (0,0) along the straight lines y = mx. (b) Now compute the limit of f(x, y) as (x, y) → (0,0) along the curves y = kx³/2 (c) Explain how the two-path test shows that this limit doesn't exist. As some final food for thought, consider how part (b) gave a definite numerical answer, and yet the limit does not exist. This is worth thinking about, even though there isn't an exercise here about that.

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