Epsilon-delta continuity visualizer

What you are seeing: the continuity of $f(x) = \sin x$ at a point $x_0$. The horizontal yellow band has half-width $\epsilon$ around $f(x_0)$; the vertical band has half-width $\delta_{\max}(\epsilon)$, the largest $\delta$ for which $|x - x_0| \lt \delta$ implies $|f(x) - f(x_0)| \lt \epsilon$. The implication holds exactly inside the box.