Home/Differential Calculus/Limit algebra/Formula2.4. Limit algebraFormulaIn 2.4. Limit algebraFormulaCopy LaTeXlimx→a[f(x)g(x)]=limx→af(x)⋅limx→ag(x)\lim_{x\to a}[f(x)g(x)]=\lim_{x\to a}f(x)\cdot\lim_{x\to a}g(x)x→alim[f(x)g(x)]=x→alimf(x)⋅x→alimg(x)TagsDifferential calculusLimitLimit algebraVariablesxxxIndependent variableaaaPoint or real constantfffFunctiongggSecond function or inner compositionRelated topicsLimit algebraFound an error? Contact us.Related formulasRelatedFormulalimx→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 sectionRelatedFormulalimx→af(x)g(x)=limx→af(x)limx→ag(x),limx→ag(x)≠0\lim_{x\to a}\frac{f(x)}{g(x)}=\frac{\lim_{x\to a}f(x)}{\lim_{x\to a}g(x)},\qquad \lim_{x\to a}g(x)\neq0x→alimg(x)f(x)=limx→ag(x)limx→af(x),x→alimg(x)=0Open formulaOpen in sectionRelatedFormulalimx→a[cf(x)]=climx→af(x)\lim_{x\to a}[cf(x)]=c\lim_{x\to a}f(x)x→alim[cf(x)]=cx→alimf(x)Open formulaOpen in sectionRelatedFormulalimx→a[f(x)]n=[limx→af(x)]n,n∈Z, limx→af(x)≠0 if n<0\lim_{x\to a}[f(x)]^n=\left[\lim_{x\to a}f(x)\right]^n,\qquad n\in\mathbb{Z},\ \lim_{x\to a}f(x)\neq 0\ \text{if }n<0x→alim[f(x)]n=[x→alimf(x)]n,n∈Z, x→alimf(x)=0 if n<0Open formulaOpen in section