analysis Definition Left-sided Limit Let f:D→R be a function. f has a left-sided limit c∈R at x0∈D if: x→x0−limf(x)=c⟺∀ε>0 ∃δ>0 ∀x∈D:(x0−δ<x<x0⟹∣f(x)−c∣<ε) or: x→x0−limf(x)=c⟺∀(xn)n∈N:(xn<x0∧n→∞limxn=x0)⟹n→∞limf(xn)=c with xn∈D.