Vanishing Point
Evaluate each limit to solidify a span of the bridge, then drag the epsilon band and tune a delta that traps the curve.
How to play
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.
- Read the function and choose the value of the limit (or DNE)
- When the limit exists, tune the epsilon band and find a delta that traps the curve
- Tighter delta bands earn a bigger bonus
- Where the limit doesn't exist, recognize the gap and route around it
Game modes
- Daily: a fixed set of six levels shared each day
- Practice: fresh randomized rounds
Controls
- Desktop: click a limit choice, drag the epsilon and delta sliders, then solidify the bridge
- Phone & tablet: tap a choice and drag the sliders by touch
Tips & strategy
- Plug the approach point into the simplified function to read the limit, watching for holes and jumps
- Shrink delta before widening epsilon — a tight delta band both traps the curve and scores higher
What you'll learn
Vanishing Point makes the epsilon-delta definition of a limit concrete, a cornerstone of calculus.
- Skills: limits, the epsilon-delta definition, calculus foundations
- Best for: advanced high school / early college
- For parents & teachers: the rigorous definition of a limit.
About Vanishing Point
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.
A free, original browser game on PlayPendium — no download, no install. Browse all games →
