You may freely use techniques from one-variable calculus, such as L'Hpital's rule.
Consider f(x, y).
f(x, y) = {
xy^3 / (x^2 + y^6) if (x, y) ≠ (0, 0)
0 if (x, y) = (0, 0)
(a) Compute the limit as (x, y) → (0, 0) of f along the path x = 0. (If an answer does not exist, enter DNE.)
(b) Compute the limit as (x, y) → (0, 0) of f along the path x = y^3. (If an answer does not exist, enter DNE.)
(c) Show that f is not continuous at (0, 0).
Since the limits as (x, y) → (0, 0) of f along the paths x = 0 and x = y^3 ---Select--- , f is not continuous at (0, 0).