# Limit

Computes the limit of a function or expression.

## Syntax

limit(Function, Identifier, Real | Infinity)

limit(Function, Real | Infinity)

limit(Function, Identifier, Real, Integer)

limit(Function, Real, Integer)


## Description

Given a function $f\left({x}_{1},...,{x}_{n}\right)$, an identifier ${x}_{i}$ and ${x}_{0}\in \mathrm{ℝ}\cup \infty$, computes the limit $\underset{{x}_{i}\to {x}_{0}}{\mathrm{lim}}f\left({x}_{1},...,{x}_{n}\right)$

Given an univariate function $f\left(x\right)$ and ${x}_{0}\in \mathrm{ℝ}\cup \infty$, computes the limit $\underset{x\to {x}_{0}}{\mathrm{lim}}f\left(x\right)$

Given a function $f\left({x}_{1},...,{x}_{n}\right)$, an identifier ${x}_{i}$, ${x}_{0}\in \mathrm{ℝ}$ and an integer $r\in \left\{-1,0,+1\right\}$, computes the limit $\underset{{x}_{i}\to {x}_{0}^{r}}{\mathrm{lim}}f\left({x}_{1},...,{x}_{n}\right)$, where ${x}_{0}^{r}$ stands for the limit for the left when $r=-1$, for above when $r=+1$ and it stands for the ordinary limit when $r=0$.

Given an univariate function $f\left(x\right)$, ${x}_{0}\in \mathrm{ℝ}$ and an integer $r\in \left\{-1,0,+1\right\}$, computes the limit $\underset{x\to {x}_{0}^{r}}{\mathrm{lim}}f\left(x\right)$, where ${x}_{0}^{r}$ stands for the limit for the left when $r=-1$, for above when $r=+1$ and it stands for the ordinary limit when $r=0$.