The precise definition of a limit

There is a more convenient form of the the precise definition of a limit tool with sliders, but it is less powerful.

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Input a function \(f(x)\). Then choose a value for \(a\), the fixed \(x\) value. Guess what the limit \(\displaystyle\lim_{x \rightarrow a} f(x)\) will be, and record your guess as \(L\) above. If your guess is correct, then the following thing should happen: Pick ANY positive number for \(\epsilon > 0\). Then, based on picking the number you did for \(\epsilon\), there should be a choice of \(\delta > 0\) (now, go find it!) so that the graph of the function avoids the red areas (with the exception of the line \(x=a\), where we don't care what happens).

This task is will be easier to do when \(\epsilon\) is large, so try picking smaller positive values for \(\epsilon\) (maybe divide it by two). If \(\epsilon\) gets smaller and smaller, you'll have to adjust by choosing \(\delta\) to be smaller and smaller. If it becomes hard to see what's going on, adjust the scale by adjusting the \(x\) and \(y\) min and max values.