for various values of n.

Try various values for n, both positive and negative integers. Also, try values for n which are not integers and which need to be entered in decimal format. Make a conjecture that you think that will happen for all values of n. Test your conjecture by choosing other values for n.

Comments:

• First, notice that we have two tables. One contains the values of x that gets closer and closer to 0 from the right or positive direction and the other table contains the values of x that gets closer and closer to 0 from the left or negative direction. The reason for including both tables is that this is the first example that has different results depending upon whether you come to 0 from the right or the left.
• This is our first example of limits that do not exist.
• Notice that many of the numbers are expressed in scientific notation.
• This program is written in Javascript. This language uses the term NaN when it cannot perform a calculation. Can you determine when this program cannot do these calculations?
• We have chosen x to be 2 plus some power of 1/10 in the left table and have chosen x to be 2 minus some power of 1/10 in the right table. N indicates this power.