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Limit in LaTeX

A limit is written with \lim, and the condition goes in the subscript with the arrow \to. In display math the condition is placed under the word lim.

Limit of a function

\lim_{x \to 0} \frac{\sin x}{x} = 1

\lim_{x \to 0} \frac{\sin x}{x} = 1

Limit of a sequence

\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e

\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e

One-sided limit

\lim_{x \to 0^{+}} \ln x = -\infty

\lim_{x \to 0^{+}} \ln x = -\infty

Common mistakes

Writing lim without a backslash: it is set in italics like the product l·i·m.
Typing -> instead of \to: in math mode you get a minus sign followed by a greater-than sign.

See also

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