# Find the following limits or state that they do not exist. \lim_{x\to4}\f

Find the following limits or state that they do not exist.
$\underset{x\to 4}{lim}\frac{{x}^{2}-16}{4-x}$
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To determine:
$\underset{x\to 4}{lim}\frac{{x}^{2}-16}{4-x}$
Formula used
${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$
Calculation
Consider $\underset{x\to 4}{lim}\frac{{x}^{2}-16}{4-x}$
$=\underset{x\to 4}{lim}\frac{{x}^{2}-{4}^{2}}{4-x}$
$=\underset{x\to 4}{lim}\frac{\left(x+4\right)\left(x-4\right)}{4-x}$
$=\underset{x\to 4}{lim}\frac{-\left(x+4\right)\left(4-x\right)}{4-x}$
$=\underset{x\to 4}{lim}-\left(x+4\right)$
$=-\left(4+4\right)=-8$
Hence, $\underset{x\to 4}{lim}\frac{{x}^{2}-16}{4-x}=-8$
Jeffrey Jordon