---
id: mat-01-limits-continuity
title: "Limits and continuity"
---

# Limits and continuity

## What is a limit
A limit describes the value that a function approaches as the input approaches a point.

## Basic limit laws
If limits exist, they follow linearity, product, quotient, and power laws.

## Special limits
Two important special limits are:
- sin x / x as x approaches 0
- (1 + 1/n)^n as n grows

## Continuity
A function is continuous at a point if the limit equals the function value.

## One sided and infinite limits
Sometimes we consider limits from the left or right, or limits that diverge to infinity.