$f(x) = x^2$stetig in $x_0 = 1$ $f(x) = \operatorname{sgn}(x)$Sprungstelle in $x_0 = 0$ $f(x) = \sin(x)/x$hebbare Lücke in $x_0 = 0$ $f(x) = \sin(1/x)$Oszillation in $x_0 = 0$ $f(x) = \lfloor x \rfloor$Sprung in $x_0 = 1$ $f(x) = 1/x$Polstelle in $x_0 = 0$

Von links: $x_n = x_0 - \tfrac{a}{n}$ Von rechts: $x_n = x_0 + \tfrac{a}{n}$ Alternierend: $x_n = x_0 + \tfrac{a \cdot (-1)^n}{n}$