---
tag: 0J8Y1NCY0K
kind: concept
name: Limit of a function of several variables
aliases: [multivariable-limit]
msc: [26B05]
uses: [0JPCHTXWG0, 0XPR1E85W0]
sources:
  - url: https://en.wikipedia.org/wiki/Limit_of_a_function
    locator: Functions of more than one variable
---

## Summary

The limit of a function of several variables at a point $a$ is the value that $f(x)$ approaches when $x$ approaches $a$ in [[Euclidean space|0XPR1E85W0]]. The approach can be from any direction and along any route.
The distance in $\mathbb{R}^n$ measures how close $x$ is to $a$.