# Evaluate the following limits. lim_{xrightarrow0}frac{tan5x}{x}

Evaluate the following limits.
$\underset{x\to 0}{lim}\frac{\mathrm{tan}5x}{x}$
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Nicole Conner
Given,
$\underset{x\to 0}{lim}\frac{\mathrm{tan}5x}{x}$
On simplification, we get
$\underset{x\to 0}{lim}\frac{\mathrm{tan}5x}{x}=\underset{x\to 0}{lim}\frac{5\mathrm{tan}5x}{5x}$
$=5\cdot \underset{x\to 0}{lim}\frac{\mathrm{tan}5x}{5x}$

$=5$
Jeffrey Jordon