# Trig limit

## Homework Statement

I want to find the limit:

$$\lim_{x\to 0}\frac{sin|x|}{x}$$

## The Attempt at a Solution

I know that the answer must be "limit doesn't exist" but I don't know how to arrive at that answer. I know that $$\lim_{x\to 0}\frac{sinx}{x}=1$$ but apparently it's a very different situation. Can anyone show me how to find this limit?

Mark44
Mentor
Look at the two one-sided limits, and see if they are the same or different.

Look at the two one-sided limits, and see if they are the same or different.

What are the two one sided limits? That's what I don't get!

Mark44
Mentor
lim x -->0+
lim x -->0-

For the first, |x| = x
For the second, |x| = -x