# Limit of absolute value

1. Sep 23, 2005

### Kamataat

Is it correct that $|\sin x|=-\sin x$ as $x\rightarrow 0-$?

It's clear for a function like $y=x$, but I ask the question since the sine oscillates from positive to negative values, so for different x's the abs. value is either pos. or neg. Or do I only need to consider values of x that are between -pi and 0?

I know the limit is zero, I just need to know how to write the intermediate step of getting rid of the abs. value sign.

- Kamataat

2. Sep 23, 2005

### TD

If you're approaching 0 from the left (so bottom, smaller values i.e. negatives) then the sine is negative there, so |sinx| indeed becomes -sinx.

3. Sep 23, 2005