# How do you find lim sinx/x as x->0 using l'Hospital's Rule?

Mar 15, 2018

${\lim}_{x \to 0} \sin \frac{x}{x} = 1$

#### Explanation:

${\lim}_{x \to 0} \sin \frac{x}{x}$ is a well known standard limit $= 1$.

Here, we are asked to use l'Hospital's rule since the limit reduces to the indeterminate form $\frac{0}{0}$

Thus, ${\lim}_{x \to 0} \sin \frac{x}{x} = {\lim}_{x \to 0} \frac{\frac{d}{\mathrm{dx}} \sin x}{\frac{d}{\mathrm{dx}} x}$

$= {\lim}_{x \to 0} \cos \frac{x}{1} = \frac{1}{1} = 1$