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\lim is an operator name, so it prints upright and places its subscript below in display math. The arrow is \to. In inline math the subscript moves to the right; add \limits to keep it underneath.
All ways to write it
| Command | Use | Package | Copy |
|---|---|---|---|
\lim_{x \to a} f(x) | limit as x approaches a | none | |
\lim_{x \to a^+} | one-sided, from the right | none | |
\lim_{n \to \infty} | limit of a sequence | none | |
\liminf | limit inferior | none | |
\limsup | limit superior | none | |
\lim\limits_{x \to a} | force subscript below in inline math | none |
Example
\lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = f'(x)The definition of the derivative.
Questions
How do I define my own operator like lim?
\operatorname{name} for one-off use, or \DeclareMathOperator{\name}{name} in the preamble (amsmath). KaTeX supports \operatorname.
Related symbols
- Infinity ∞
\infty - Arrows →
\rightarrow - Derivatives ′
\frac{dy}{dx}
Using limit in Confluence
Confluence Cloud has no built-in LaTeX. With LaTeX Math for Confluence you add a math macro to any page, type \lim_{x \to a} f(x) and it renders inline or as a block, with a live preview while you edit. Every command on this page renders there without extra packages.