limits #

Shows x approaching a from the left and right while f(x) approaches a single value L, even when the function’s value at x=a is different (a hole at (a,L) and a filled point at (a,f(a))). The animation slows near a to emphasize “arbitrarily close” without reaching the point, and highlights that the two-sided limit exists when left- and right-hand limits match.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Checking continuity and identifying removable discontinuities
02.Reasoning about behavior near singularities or breakpoints in models
03.Foundation for defining derivatives and integrals in calculus

technical notes #

Renders a piecewise visualization with an open circle at (a,L) and a filled square at (a,f(a)); two animated markers approach a from both sides using cubic easing. Uses grid-snapped coordinates for a blocky aesthetic, green-on-black palette, and responsive scaling via baseSize.

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