# Evaluate the following limits. lim_{(x,y)rightarrow(1,-1)}frac{10uv-2v^2}{u^2+v^2}

Evaluate the following limits. $\underset{\left(x,y\right)\to \left(1,-1\right)}{lim}\frac{10uv-2{v}^{2}}{{u}^{2}+{v}^{2}}$
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okomgcae
The given expression is $\underset{\left(x,y\right)\to \left(1,-1\right)}{lim}\frac{10uv-2{v}^{2}}{{u}^{2}+{v}^{2}}$
$\underset{\left(x,y\right)\to \left(1,-1\right)}{lim}\frac{10uv-2{v}^{2}}{{u}^{2}+{v}^{2}}=\frac{10\left(1\right)\left(-1\right)-2\left(-1{\right)}^{2}}{\left(1{\right)}^{2}+\left(-1{\right)}^{2}}$
$=\frac{-10-2}{2}$
$=\frac{-12}{2}$
$=-6$
Jeffrey Jordon