SOLUTION: Find limit of function (x² - x - 6)/|x - 3| when x approaches to 3? Note: Here | | means absolute.

The function is  .


In vicinity of  x= 3, the function is simply  +/- (x+2),

where the sign  " + "  works on the right of x= 3

and   the sign  " - "  works on the  left of x= 3.



Thus the limit is 5 from the right side and  -5 from the left side.


The function is DISCONTINUOUS at x = 3,  so the two-sided limit DOES NOT exist.



                        Visual check



    


                  Plot y =