continuity #

Shows continuity at x=a as a 3-item checklist: (1) f(a) is defined (filled point), (2) the limit exists (left/right approach markers agree), and (3) the limit equals the function value. The animation cycles through broken cases (a hole or a jump) and then smoothly fixes them so lim_{x->a} f(x)=f(a).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Diagnose discontinuities in piecewise functions (holes vs jumps).
02.Understand when limit computations actually tell you the function’s value.
03.Justify when calculus rules (like plugging in for polynomials) apply because the function is continuous.

technical notes #

Pure Canvas2D. Uses a snapped grid for a blocky aesthetic, time-based phases to highlight the three continuity conditions, and alternates between removable/jump discontinuities before easing into a corrected continuous function. Responsive scaling via scale = min(w,h)/baseSize.

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