Exploration.

Set up the formulas for the piecewise function  .  

                              The  left-hand and right-hand limits at  ,  ,  and    are easily determined:

        At  ,  the left-hand limit is  

                    ,     
                    
and the right-hand limit is  
                    
                    .

This computation can be done with Mathematica.

The Maple commands are similar  

  

                                                              


  

                                                              

        At  ,  the left-hand limit is  

                    ,

and the right-hand limit is  

                    .

This computation can be done with Mathematica.

The Maple commands are similar  

  

                                                              


  

                                                              

        At  ,  the left-hand limit is  

                    ,

and the right-hand limit is  

                    .

This computation can be done with Mathematica.

The Maple commands are similar  

  

                                                              


  

                                                              

Remark.  For this example, one sided limits will exist at the endpoints  .  

        At  ,  the right-hand limit is  

                    .

This computation can be done with Mathematica.

The Maple command is similar  



                                                              

        At  ,  the left-hand limit is   

                    .

This computation can be done with Mathematica.

The Maple command is similar  

  

                                                              

(c) 2010 John H. Mathews, Russell W. Howell