# LaTeX limit symbols (lim inf, lim sup, inj lim, proj lim)

Symbol Command
$\lim$ \lim
$\liminf$ \liminf
$\limsup$ \limsup
$\injlim$ \injlim
$\projlim$ \projlim
$\plim$ \plim
Symbol Command
$\varinjlim$ \varinjlim
$\varprojlim$ \varprojlim
$\varliminf$ \varliminf
$\varlimsup$ \varlimsup

## Inline mode

$\lim_{x \to 3} x^2$ is 9.


$\lim_{x \to 3} x^2$ is 9.

$\lim_{x \to \infty} \frac{1}{x}$ is 0.


$\lim_{x \to \infty} \frac{1}{x}$ is 0.

## Display mode

$\lim_{x \to 3} f(x) \\~\\ \lim_{x \to 3^{+}} f(x) \\~\\ \lim_{x \to 3^{-}} f(x)$


$\lim_{x \to 3} f(x) \\~\\ \lim_{x \to 3^{+}} f(x) \\~\\ \lim_{x \to 3^{-}} f(x)$

$\lim_{x \uparrow a} f(x) \\~\\ \lim_{x \downarrow a} f(x) \\~\\ \lim_{x \nearrow a} f(x) \\~\\ \lim_{x \searrow a} f(x)$


$\lim_{x \uparrow a} f(x) \\~\\ \lim_{x \downarrow a} f(x) \\~\\ \lim_{x \nearrow a} f(x) \\~\\ \lim_{x \searrow a} f(x)$

$\liminf_{x \to a} f(x) \\~\\ \limsup_{x \to a} f(x)$


$\liminf_{x \to a} f(x) \\~\\ \limsup_{x \to a} f(x)$

## Substack

You can write the limit with multiple lines in a subscript to use \substack.

$\lim_{ \substack{ x \to 0 \\ n \to \infty } } x^{\log n}$


$\lim_{ \substack{ x \to 0 \\ n \to \infty } } x^{\log n}$