# Evaluate the limit, if it exist. lim_{x to 0} {sin 5 x} / {2 x}.

## Question:

Evaluate the limit, if it exist.

{eq}\displaystyle \lim_{x \to 0} \dfrac {\sin 5 x} {2 x} {/eq}.

## Limits:

We have a function that has a sine term and a linear term. We have many methods to evaluate the limits but here we will use the standard limit formula.

$$\displaystyle \lim_{x \to 0} \dfrac {\sin 5 x} {2 x}\\$$

We can write it as:

$$\displaystyle \lim_{x \to 0}\frac{5}{2}\frac{\sin (5x)}{5x}\\$$

We will use the standard limit formula:

$$\lim_{x\rightarrow 0}\frac{\sin x}{x}=1\\$$

So we get the answer as:

$$\frac{5}{2}$$

The limit exists and has a finite value: