Dustinsfl
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$f(x,y) = \begin{cases}(x + y)\sin\frac{1}{x}\sin\frac{1}{y}, & \text{if } x\neq 0\text{ and } y\neq 0\\
0, & \text{if } x = 0\text{ or } y = 0\end{cases}$ We can re-write $f$ as
$$
f(x,y) = \begin{cases}
\frac{x + y}{xy}\frac{\sin\frac{1}{x}\sin\frac{1}{y}}{\frac{1}{x}\frac{1}{y}}, & \text{if } x\neq 0\text{ and } y\neq 0\\
0, & \text{if } x = 0\text{ or } y = 0\end{cases}
$$
Can I use L'Hopitals rule here? Taking the limit gives 0/0. I am looking for points of discontinuity if any exist in $f$.
0, & \text{if } x = 0\text{ or } y = 0\end{cases}$ We can re-write $f$ as
$$
f(x,y) = \begin{cases}
\frac{x + y}{xy}\frac{\sin\frac{1}{x}\sin\frac{1}{y}}{\frac{1}{x}\frac{1}{y}}, & \text{if } x\neq 0\text{ and } y\neq 0\\
0, & \text{if } x = 0\text{ or } y = 0\end{cases}
$$
Can I use L'Hopitals rule here? Taking the limit gives 0/0. I am looking for points of discontinuity if any exist in $f$.