Home/Differential Calculus/Notable limits/Formula2.5. Notable limitsFormulaIn 2.5. Notable limitsFormulaCopy LaTeXlimx→01−cosxx=0\lim_{x\to0}\frac{1-\cos x}{x}=0x→0limx1−cosx=0TagsDifferential calculusLimitNotable limitsVariablesxxxIndependent variableFound an error? Contact us.Related formulasRelatedFormulalimx→0\sinxx=1\lim_{x\to0}\frac{\sinx}{x}=1x→0limx\sinx=1Open formulaOpen in sectionRelatedFormulalimx→0ex−1x=1\lim_{x\to0}\frac{e^x-1}{x}=1x→0limxex−1=1Open formulaOpen in sectionRelatedFormulalimx→0ln(1+x)x=1\lim_{x\to0}\frac{\ln(1+x)}{x}=1x→0limxln(1+x)=1Open formulaOpen in sectionRelatedFormulalimx→0(1+x)1/x=e\lim_{x\to0}(1+x)^{1/x}=ex→0lim(1+x)1/x=eOpen formulaOpen in sectionRelatedFormulalimx→∞(1+1x)x=e\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x=ex→∞lim(1+x1)x=eOpen formulaOpen in section