Limits of Sequences and Functions, Continuity

MathematicsFunctions & GraphsAges 16–17

Sequence mode: the points (n, uₙ) approach the line y = L; a draggable band L ± ε shows that from some index N₀ onward every term stays inside the band. Function mode: drag x toward x₀ from both sides to watch f(x) approach the left- and right-hand limits, spot a discontinuity or a point where the function is undefined at x₀, and draw a conclusion about continuity.