# Find the limit and discuss the continuity of the function. \lim_{(x,y)\to

Find the limit and discuss the continuity of the function.
$\underset{\left(x,y\right)\to \left(-1,2\right)}{lim}\frac{x+y}{x-y}$
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Cullen
Consider the given limit $\underset{\left(x,y\right)\to \left(-1,2\right)}{lim}\frac{x+y}{x-y}$
Now find the limit
$\underset{\left(x,y\right)\to \left(-1,2\right)}{lim}\frac{x+y}{x-y}=\frac{-1+2}{-1-2}$
$=\frac{1}{-3}$
$=-\frac{1}{3}$
So limit is $\underset{\left(x,y\right)\to \left(-1,2\right)}{lim}\frac{x+y}{x-y}=-\frac{1}{3}$
Condition for continuity $\underset{\left(x,y\right)\to \left(a,b\right)}{lim}f\left(x,y\right)=f\left(a,b\right)$
Find the value of the function at the given limit point
$f\left(x,y\right)=\frac{x+y}{x-y}$
$f\left(-1,2\right)=\frac{-1+2}{-1-2}$
$=\frac{1}{-3}$
$=-\frac{1}{3}$
So, $\underset{\left(x,y\right)\to \left(-1,2\right)}{lim}\frac{x+y}{x-y}=f\left(-1,2\right)=-\frac{1}{3}$
Hence function is continuous at the given limit point