Question on limits

[BAndrew]

I have a question about calculating limits with absolute values. I don't want the solution.



Say for example

 

 

 

 

sign of x² - 1



___x|_-∞_____-1__+__1______________+∞

x² -1|_____+___0__-__ 0________+________







sign of x² + 2x - 3



_______x |_-∞_______-3____ 1_______+∞

x² + 2x -3 |_____+_____0__-__0___+___



Now my question is how you handle absolutes



for example

 

 

 

in this case:

|x² - 1| = x² - 1 or -(x² - 1) [explain why]

|x² + 2x - 3| = x² + 2x - 3 or -(x² + 2x - 3) [explain why]

 

 

 

 

 

in this case:



|x² - 1| = x² - 1 or -(x² - 1) [explain why]

|x² + 2x - 3| = x² + 2x - 3 or -(x² + 2x - 3) [explain why]

 

 

Thanks in advance.

 

EDIT: It's lim

x->1

Edited March 6, 2013 by BAndrew

[imatfaal]

Well my first comment was that upon initial inspection (and quick check) that neither the top expression nor the bottom ever have negative values - so your signs are clear whatever the limit. Once you know your signs it just becomes a job of deciding what happens as you approach 1