In a series cutting experiments, Jimmy summarized the relationship between force to cut the material and the heat released from the material. The heat is a piecewise continuous function of force. He wants to analysis the heat released when force is 1 and 2 kN. The function is:

Since f(x) is a piecewise function, the functions for f(x) on the left and right hand side of 1 kN and 2 kN. The way to analysis the boundary heat conductive is to consider both side heat conductive at the boundary.

First, consider the case of x approaches 1^-:

     

Second, consider the case of x approaches 1⁺:

     

Third, consider the case of x approaches 2^-:

Finally, consider the case of x approaches 2⁺:

     

• According to left and right hand limit,
  

       

            
  In this situation, although both left and right hand limit exist, the limit at 1 kN does not exist. The heat conductive function is not a continuous function at this point. The function has a jump. The same situation happens at 2 kN.

• In order to solve the limit of a function, many limit laws can be applied. The proper application of the limit law can make the problem solving process easier. Of course, it does take practice.