Explore the limit

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.