# Limit and Continuity Find the limit (if it exists) and discuss the continuity of

Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.
$\underset{\left(x,y\right)\to \left(1,1\right)}{lim}\frac{xy}{{x}^{2}+{y}^{2}}$
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Jaylen Fountain

We have,
$\underset{\left(x,y\right)\to \left(1,1\right)}{lim}\frac{xy}{{x}^{2}+{y}^{2}}$
$=\frac{\left(1\right)\left(1\right)}{1+1}$
$=\frac{1}{2}$
Clearly the function $f\left(x,y\right)=\frac{xy}{{x}^{2}+{y}^{2}}$ is defined everywhere except at (0,0). Thus f(x,y) is continuous everywhere except at (0,0)