Limit Explorer

Visualize limits, one-sided limits, and the epsilon-delta definition

Function Examples

Custom Function

Visualization

The hollow circle shows the limit point. Dashed line shows the limit value.

Limit Analysis

Function: (x²-4)/(x-2) as x → 2

Left Limit (x → a⁻)
4.000
Right Limit (x → a⁺)
4.000
Two-Sided Limit
4.000
f(a) - Actual Value
undefined
Continuity Status: Removable Discontinuity

Epsilon-Delta Visualization

The ε-δ definition: For all ε > 0, there exists δ > 0 such that:

0 < |x - a| < δ ⟹ |f(x) - L| < ε

Numerical Approach

x (approaching from left) f(x) x (approaching from right) f(x)