Home/Differential Calculus/One-sided limits/Formula2.3. One-sided limitsFormulaIn 2.3. One-sided limitsFormulaCopy LaTeXlimx→a−f(x)=LL,limx→a+f(x)=LR\lim_{x\to a^-}f(x)=L_L,\qquad \lim_{x\to a^+}f(x)=L_Rx→a−limf(x)=LL,x→a+limf(x)=LRTagsDifferential calculusLimitOne-sided limitsExplore the ideaExplore the ideaVariablesxxxIndependent variableaaaPoint or real constantfffFunctionLLLLimit valueConditionslimx→a+f(x)=LR\lim_{x\to a^+}f(x)=L_Rlimx→a+f(x)=LRFound an error? Contact us.Related formulasRelatedFormulalimx→af(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<ε\lim_{x\to a}f(x)=L \quad\Longleftrightarrow\quad \forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilonx→alimf(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<εOpen formulaOpen in sectionRelatedFormulalimx→af(x)=L⟺LL=LR=L\lim_{x\to a}f(x)=L \quad\Longleftrightarrow\quad L_L=L_R=Lx→alimf(x)=L⟺LL=LR=LOpen formulaOpen in section