## anonymous one year ago Lim x goes to 1 x^2-1/|x-1| anyone can find this limit?

1. anonymous

$\lim_{x\to 1}\frac{x^2-1}{|x-1|}$

2. anonymous

seems unlikely since this is is a piecewise function it is one thing if $$x>1$$ and quite another if $$x<1$$

3. anonymous

if $$x>1$$ then $$|x-1|=x-1$$ when you factor and cancel you get $x+1$

4. anonymous

you get something else if $$x<1$$ try it and see

5. anonymous

I wonder if I should use left and right limit to do this

6. anonymous

you have no choice but to do that, since $$|x-1|$$ is a piecewise function which changes definition at $$x=1$$

7. anonymous

lets take it step by step

8. anonymous

if $$x>1$$ then $$|x-1|=x-1$$ right?

9. anonymous

did i lose you there?

10. anonymous

im here

11. anonymous

if $$x>1$$ then $$|x-1|=x-1$$so your function is $\frac{x^2-1}{x-1}=\frac{(x+1)(x-1)}{x-1}=x+1$ making the limit as $$x\to 1^+=1+1=2$$

12. anonymous

I see, now the left limit I guess

13. anonymous

left limit is different because if $$x<1$$ then $$|x-1|=1-x$$

14. anonymous

so the limit doesnt exist right

15. anonymous

no the two sided limit does not exist

16. anonymous

i see

17. anonymous

Thank you