What is the limit of sin|x|/x as x approaches 0?

[math2010]

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]

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

 

[math2010]

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]

lim x -->0⁺
lim x -->0^-

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