# How do you find lim sin(2x)/x as x->0 using l'Hospital's Rule?

${\lim}_{x \to 0} \sin \frac{2 x}{x} = 2$
${\lim}_{x \to 0} \sin \frac{2 x}{x}$ is in the indeterminate form $\frac{0}{0}$ so we can solve it using l'Hospital's rule:
${\lim}_{x \to 0} \sin \frac{2 x}{x} = {\lim}_{x \to 0} \frac{\frac{d}{\mathrm{dx}} \sin \left(2 x\right)}{\frac{d}{\mathrm{dx}} x} = {\lim}_{x \to 0} \frac{2 \cos \left(2 x\right)}{1} = 2$