Recall the definition of a limit: we say [math] if:

For all [math] there exists a [math] such that [math] whenever [math].

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

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

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

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