I can't find the limit absolute value function.

1. Nov 22, 2012

Vola

How find the limit of absolute value function?

Hi everybody,

I can't find the limit of (abs(x-2)-2)/x as x-->1.
I know it's (-1) but I don't see how you get to it.
If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1.
However according to the graph two sided limit does exist and it's (-1).

Thanks

Last edited: Nov 22, 2012
2. Nov 22, 2012

Ray Vickson

What happens when x is near 1?

RGV

3. Nov 22, 2012

Vola

is it just a "plug-in" problem?

(|1-2|-2)/1 => (|-1|-2)/1 => (1-2)/1 =-1?

Last edited: Nov 22, 2012
4. Nov 22, 2012

Ray Vickson

RGV

5. Nov 22, 2012

Vola

The value of function is negative(?)

6. Nov 22, 2012

Ray Vickson

Let me ask it one last time: if f(x) = (|x-2|-2)/x, what would be the simplified formula for f(x) when x is near 1? Don't guess---calculate!

RGV

7. Nov 22, 2012

Vola

f(x)=-1

8. Nov 23, 2012

HallsofIvy

Good! For all x less than 2, f(x)= -1 so the limit at any x less than two is -1.

But you don't "take (x- 2)> 0"! That would be x> 2 and you want the limit at x= 1. You can't "go to 1" if keep x> 2.

9. Nov 23, 2012

Vola

thank you HallsofIvy and Ray