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, 201312 yr by BAndrew

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