# How do you find the limit lim_(x->0)sin(x)/x ?

Aug 18, 2014

We will use l'Hôpital's Rule.

l'Hôpital's rule states:

${\lim}_{x \to a} f \frac{x}{g} \left(x\right) = {\lim}_{x \to a} \frac{f ' \left(x\right)}{g ' \left(x\right)}$

In this example, $f \left(x\right)$ would be $\sin x$, and $g \left(x\right)$ would be $x$.

Thus,

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

Quite clearly, this limit evaluates to $1$, since $\cos 0$ is equal to $1$.