Home/Differential Calculus/Limits/One-sided limitsSection 2.3One-sided limitsFormulavizCopy 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)=LRlimx→a+f(x)=LR\lim_{x\to a^+}f(x)=L_Rlimx→a+f(x)=LRView detail →FormulaCopy 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=LThe two-sided limit exists iff the one-sided limits agree.⟺\Longleftrightarrow⟺LL=LR=LL_L=L_R=LLL=LR=LView detail →
FormulavizCopy 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)=LRlimx→a+f(x)=LR\lim_{x\to a^+}f(x)=L_Rlimx→a+f(x)=LRView detail →
FormulaCopy 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=LThe two-sided limit exists iff the one-sided limits agree.⟺\Longleftrightarrow⟺LL=LR=LL_L=L_R=LLL=LR=LView detail →