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\begin{center}
\textbf{Partial Differentiation}

\textit{\textbf{Limits}}
\end{center}

\textbf{Question}

Evaluate the given limit. If the limit does not
exist, explain why.

$$ \lim_{(x,y)\to(0,0)} \frac{y^3}{x^2+y^2}$$


\textbf{Answer}

$$\ds \left | \frac{y^3}{x^2+y^2} \right | \le \frac{y^2}{x^2+y^2}|y|
\le |y| \to 0$$
as $(x,y)\to (0,0)$.

$\Rightarrow \ds \lim_{(x,y)\to(0,0)} \frac{y^3}{x^2+y^2}=0$


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