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