Recall the definition of a limit: we say if:

For all there exists a such that whenever .

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:

You can earn partial credit on this problem.