Limit in LaTeX (\lim_{x \to \infty})

Where it is used

Writes the limit operator with x approaching infinity placed beneath "lim".

\lim is a predefined operator name, so it prints in upright roman and, in display math, places the subscript x \to \infty directly below. Inline, the subscript moves to the side to keep line spacing tidy. The arrow inside is \to, a short alias for \rightarrow. One-sided limits are written x \to 0^+ or x \downarrow 0. Related operators \limsup and \liminf work the same way. If you need a custom limit-like word with stacked subscripts, define it with \DeclareMathOperator* (the star enables limits) rather than writing \text{lim}.

Also listed under: Calculus & Analysis

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Limit: $\lim_{x \to \infty}$

\[ \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^{x} = e \]
\end{document}

Related symbols

• Infinity\infty
• Integral\int_{a}^{b}
• Approximately Equal\approx
• Product\prod_{i=1}^{n}
• Not Equal\neq
• Summation\sum_{i=1}^{n}

Frequently asked questions

How do I write Limit in LaTeX?

Type \lim_{x \to \infty} in math mode, for example $\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^{x} = e$. It works in plain LaTeX without loading any package.

Which package do I need for \lim_{x \to \infty}?

None. \lim_{x \to \infty} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \lim_{x \to \infty} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\lim_{x \to \infty}$ in running text.