Here we will look at the above function , which has no limit at 1.
Therefore the claim that is false, meaning the above
definition fails.

First show that for some values of , there are values of satisfying the conclusion
of the limit definition. For example:

If then provide a value for making the conclusion of the limit definition
true:

However, not every value of will work. Use the applet to find a value
for such that no will satisfy the conclusion of the limit definition, and record that
here: