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.

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

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

LaTeX calculus

LaTeX