Understanding Limits: Why |h|/h Approaches -1 as h Approaches 0

[ratios]

Hello all,

I don't understand why |h|/h will become -1 as h approches 0 from the left. I can see how the numerator becomes negative, as |x| = -x if x< 0, but shouldn't the denominator become negative also since h < 0 when we approach 0 from the left? So why isn't the answer -h/-h = 1?

 

[StatusX]

The numerator is always positive. It's true that |x|=-x when x<0, but in that case -x>0, and |x|/x=-x/x=-1.

 

[Hurkyl]

I can see how the numerator becomes negative, as |x| = -x if x< 0

You see wrong. Here, -x is positive.

 

[ratios]

Okay I see. Thanks for the help!