ε–δ Limit Explorer

Play with ε and watch the matching δ respond so that |x−a| < δ ⇒ |f(x)−L| < ε.

Function $f(x)$

Point $a$ (approach point)

Choose $\varepsilon$ (epsilon)

Computed limit $L$

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Matching $\delta$

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Tip: Try Removable with $a=1$. The limit exists ($L=2$) even though $f(1)$ is undefined—ε–δ talks only about values near $a$, not at $a$.

ε-band is the horizontal strip $L-\varepsilonδ-band is the vertical strip $a-\delta