Calculus
Lab: one δ for one point or for all?
Choose ε and compare pointwise and uniform continuity. Move the center or construct point pairs disproving a proposed global δ.
Requirement, choice of δ and reason
One second per step. Local/uniform comparison visits 21 demonstration centers; counterexamples use δₖ=proposed δ/(1+k). The mathematical domain remains the stated one, not just the plotted window.
Zoomed window around the points
Axes show differences from the center: x−x₀ and f(x)−f(x₀). Gray point = center; red point = second input.
Displayed pair values
Comparison of sufficient choices at different centers
These are sufficient choices, not necessarily the largest possible. Shrinking local choices alone do not prove nonuniformity: the counterexample pairs do.
Guarantees come from formulas, not plot sampling. Floating-point plots may miss oscillations and are not proofs. The orange band is open: its boundaries correspond to difference ε.