Exercises

1. For the functions and values of a given below, go through the following steps.
   

   i.

   Find whether the exists or not. If it does, determine the limit.

   ii.

   For the limits that exist, find a value of that works for .

   1. 

   2. 

   3. 

   4. 

2. Find the right- and left-hand limits of the following function at x=1. Also, plot the function and relate your limits to the graph.

   

   Does exist? Explain your reasoning.

3. Suppose that the function is defined by

   

   where a and b are parameters. Can you find values for a and b that will make continuous at x=0? Justify your answer.