Function & Limit Explorer
Plot and evaluate functions, compose them, test continuity at a point, and evaluate limits by watching both-sided approach tables converge. Covers §5.1–5.2 and §5.16–5.17 of the calculus material.
Grapher
f in steel, g in gold (dashed), f∘g in red. FIG. T23-1
Limit by Approach Table
x → a from both sides at shrinking distances 10⁻¹ … 10⁻⁶ — the table converging to a common value is the limit.
Continuity at a needs three things at once: f(a) exists, the limit as x → a exists (left = right), and the two are equal. A jump breaks the second condition; a removable hole breaks the third.