# How do you find the limit of (sin²x)/(x) as x approaches 0?

Aug 2, 2016

0

#### Explanation:

lim_(x to 0) (sin²x)/(x)

${\lim}_{x \to 0} \frac{\sin x}{x} \cdot \sin x$

${\lim}_{x \to 0} \frac{\sin x}{x} \cdot {\lim}_{x \to 0} \sin x$, we can seperate because sin x is continuous through the limit

$= 1 \cdot 0 = 0$

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

OR

lim_(x to 0) (sin²x)/(x)

is $\frac{0}{0}$ indeterminate, so we can use L'Hopital

$= {\lim}_{x \to 0} \frac{2 \sin x \cos x}{1}$

$= {\lim}_{x \to 0} \sin 2 x = 0$