Consider the function .

(a) Fill in the following table of values for :


(b) Based on your table of values, what would you expect the limit of as approaches zero to be?

(c) Graph the function to see if it is consistent with your answers to parts (a) and (b). By graphing, find an interval for near zero such that the difference between your conjectured limit and the value of the function is less than 0.01. In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window?

You can earn partial credit on this problem.