Evaluate each limit to solidify a span of the bridge, then drag the epsilon band and tune a delta that traps the curve.
Each level shows a function and a point it approaches. First pick the value the limit converges to. If the limit exists, you then drag epsilon and delta sliders until the curve is caught inside the band, solidifying the bridge; if the limit doesn't exist, you route around the gap instead.
Vanishing Point makes the epsilon-delta definition of a limit concrete, a cornerstone of calculus.
Choosing a limit's value and then dragging epsilon and delta until the definition is satisfied is the (ε, δ) definition of a limit made operable.
Making you produce a delta for a given epsilon is the original demand.
That order is the whole definition and the reason it is hard. The challenge comes first — for every epsilon, however small — and the response second, so a limit exists only if you can always answer. Dragging the sliders is the only way most people ever feel the quantifiers.
Vanishing Point is an original free browser math game that makes the epsilon-delta definition of a limit tangible, letting you feel how narrowing the interval around a point pins the curve to its limit.