Question

MACT 2123 Spring 2023 Problem 4. (6+5+2 pts) Consider the function: \begin{equation} g(x, y) = \begin{cases} \frac{x^2|y|}{x^3+y^2} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases} \end{equation} a. Where is the function $g$ continuous? Justify your answer.

          MACT 2123                                                              Spring 2023
Problem 4. (6+5+2 pts) Consider the function:
\begin{equation*}
g(x, y) = \begin{cases}
\frac{x^2|y|}{x^3+y^2} & \text{if } (x, y) \neq (0, 0) \\
0 & \text{if } (x, y) = (0, 0)
\end{cases}
\end{equation*}
a. Where is the function $g$ continuous? Justify your answer.

MACT 2123 Spring 2023
Problem 4. (6+5+2 pts) Consider the function:

g(x, y) = (x^2|y|)/(x^3+y^2) if (x, y) ≠ (0, 0)

0 if (x, y) = (0, 0)

a. Where is the function g continuous? Justify your answer.

Added by Michael A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shubham Sharma

03/06/2022

Step 1

Step 1: The function $g(x, y)$ is continuous for all $(x, y) \neq (0, 0)$ because it is a rational function and the denominator is non-zero for all $(x, y) \neq (0, 0)$. Show more…

Show all steps

Thanks for your feedback!

МАСТ 2123 Problem 4. (6+5+2 pts) Consider the function: $$g(x, y) = \begin{cases} \frac{x^2|y|}{x^3 + y^2} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases}$$ a. Where is the function g continuous? Justify your answer. Spring 2023