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3. [-/3 Points] DETAILS MY NOTES MARSVECTORCALC6 2.2.006. You may freely use techniques from one-variable calculus, such as L'Hôpital's rule. Consider $f(x, y)$. $f(x, y) = \begin{cases} \frac{xy^3}{x^2 + y^6} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases}$ (a) Compute the limit as $(x, y) \to (0, 0)$ of $f$ along the path $x = 0$. (If an answer does not exist, enter DNE.) (b) Compute the limit as $(x, y) \to (0, 0)$ 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 $(x, y) \to (0, 0)$ of $f$ along the paths $x = 0$ and $x = y^3$ are not equal, $f$ is not continuous at $(0, 0)$.

          3. [-/3 Points]
DETAILS
MY NOTES
MARSVECTORCALC6 2.2.006.
You may freely use techniques from one-variable calculus, such as L'Hôpital's rule.
Consider $f(x, y)$.
$f(x, y) = \begin{cases} \frac{xy^3}{x^2 + y^6} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases}$
(a) Compute the limit as $(x, y) \to (0, 0)$ of $f$ along the path $x = 0$. (If an answer does not exist, enter DNE.)
(b) Compute the limit as $(x, y) \to (0, 0)$ 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 $(x, y) \to (0, 0)$ of $f$ along the paths $x = 0$ and $x = y^3$ are not equal, $f$ is not continuous at $(0, 0)$.

3. [-/3 Points]
DETAILS
MY NOTES
MARSVECTORCALC6 2.2.006.
You may freely use techniques from one-variable calculus, such as L'Hôpital'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 are not equal, f is not continuous at (0, 0).

Added by Emilio C.

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