Answer
1
Work Step by Step
We find:
\[
\lim _{(x, y) \rightarrow(0,0)} \frac{\sin \left(x^{2}+y^{2}\right)}{x^{2}+y^{2}}
\]
Given that if $(x, y) \rightarrow(0,0)$, then $z \rightarrow 0$, so we re-write the equation:
\[
\begin{array}{l}
=\lim _{z \rightarrow 0} \frac{\sin z}{z} \\
=1
\end{array}
\]
