# Evaluate the following limits. lim_{xrightarrow2}frac{sin(x-2)}{x^2-4}

Evaluate the following limits.
$\underset{x\to 2}{lim}\frac{\mathrm{sin}\left(x-2\right)}{{x}^{2}-4}$
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estenutC

Given limit is
$\underset{x\to 2}{lim}\frac{\mathrm{sin}\left(x-2\right)}{{x}^{2}-4}$
Solve,
$\underset{x\to 2}{lim}\frac{\mathrm{sin}\left(x-2\right)}{{x}^{2}-4}=\underset{x\to 2}{lim}\frac{\mathrm{sin}\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}$
$=\underset{x\to 2}{lim}\left(\frac{\mathrm{sin}\left(x-2\right)}{\left(x-2\right)}\right)\underset{x\to 2}{lim}\left(\frac{1}{x+2}\right)$
$=1×\left(\frac{1}{4}\right)$  $=\frac{1}{4}$

Jeffrey Jordon