極限の一覧
If lim x → c f ( x ) = L 1 and lim x → c g ( x ) = L 2 then: {\displaystyle {\mbox{If }}\lim _{x\to c}f(x)=L_{1}{\mbox{ and }}\lim _{x\to c}g(x)=L_{2}{\mbox{ then:}}} lim x → c [ f ( x ) ± g ( x ) ] = L 1 ± L 2 {\displaystyle \lim _{x\to c}\,[f(x)\pm g(x)]=L_{1}\pm L_{2}} lim x → c [ f ( x ) g ( x ) ] = L 1 × L 2 {\displaystyle \lim _{x\to c}\,[f(x)g(x)]=L_{1}\times L_{2}} lim x → c f ( x ) g ( x ) = L 1 L 2 if L 2 ≠ 0 {\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}={\frac {L_{1}}{L_{2}}}\qquad {\mbox{ if }}L_{2}\neq 0} lim x → c f ( x ) n = L 1 n if n is a positive integer {\displaystyle \lim _{x\to c}\,f(x)^{n}=L_{1}^{n}\qquad {\mbox{ if }}n{\mbox{ is a positive integer}}} lim x → c f ( x ) 1 n = L 1 1 n if n is a positive integer, and if n is even, then L 1 > 0 {\displaystyle \lim _{x\to c}\,f(x)^{1 \over n}=L_{1}^{1 \over n}\qquad {\mbox{ if }}n{\mbox{ is a positive integer, and if }}n{\mbox{ is even, then }}L_{1}>0}