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.
- 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.
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.