極限の一覧
lim x → c a = a {\displaystyle \lim _{x\to c}a=a}
lim x → c x = c {\displaystyle \lim _{x\to c}x=c}
lim x → c ( a x + b ) = a c + b {\displaystyle \lim _{x\to c}(ax+b)=ac+b}
lim x → c x r = c r if r is a positive integer {\displaystyle \lim _{x\to c}x^{r}=c^{r}\qquad {\mbox{ if }}r{\mbox{ is a positive integer}}}
lim x → + 0 1 x r = + ∞ {\displaystyle \lim _{x\to +0}{\frac {1}{x^{r}}}=+\infty }
lim x → − 0 1 x r = { − ∞ , if r is odd + ∞ , if r is even {\displaystyle \lim _{x\to -0}{\frac {1}{x^{r}}}=\left\{{\begin{matrix}-\infty ,&{\mbox{if }}r{\mbox{ is odd}}\\+\infty ,&{\mbox{if }}r{\mbox{ is even}}\end{matrix}}\right.}