Home/Differential Calculus/One-sided limits/Formula2.3. One-sided limitsFormulaIn 2.3. One-sided limitsFormulaCopy LaTeXlimx→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=LTagsDifferential calculusLimitOne-sided limitsDetailThe two-sided limit exists iff the one-sided limits agree.VariablesxxxIndependent variableaaaPoint or real constantfffFunctionLLLLimit valueConditions⟺\Longleftrightarrow⟺LL=LR=LL_L=L_R=LLL=LR=LFound an error? Contact us.Related formulasRelatedFormulalimx→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)=LROpen formulaOpen in sectionRelatedFormulalimx→a[f(x)±g(x)]=limx→af(x)±limx→ag(x)\lim_{x\to a}[f(x)\pm g(x)]=\lim_{x\to a}f(x)\pm\lim_{x\to a}g(x)x→alim[f(x)±g(x)]=x→alimf(x)±x→alimg(x)Open formulaOpen in section