# Evaluate the following limits. lim_{(x,y)rightarrow(-3,3)}(4x^2-y^2)

Evaluate the following limits.
$\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(4{x}^{2}-{y}^{2}\right)$
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Nichole Watt
Given:
$\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(4{x}^{2}-{y}^{2}\right)$
Solve:
$\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(4{x}^{2}-{y}^{2}\right)$
$=\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left({2}^{2}{x}^{2}-{y}^{2}\right)$
Apply exponent rule: ${a}^{n}{b}^{n}=\left(ab{\right)}^{n}$
$\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(\left(2x{\right)}^{2}-{y}^{2}\right)$
Apply $\left({x}^{2}-{y}^{2}\right)=\left(x+y\right)\left(x-y\right)$
$=\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(2x+y\right)\left(2x-y\right)$
Plug the values
$=\left(2\left(-3\right)+3\right)\left(2\left(-3\right)-3\right)$
$=\left(-6+3\right)\left(-6-3\right)$
$\left(-3\right)\left(-9\right)$
$=27$
$=\underset{\left(x,y\right)\to \left(-3,3\right)}{lim}\left(4{x}^{2}-{y}^{2}\right)=27$
Jeffrey Jordon