Table of Contents

## What are the 3 rules of continuity?

**Note that in order for a function to be continuous at a point, three things must be true:**

- The limit must exist at that point.
- The function must be defined at that point, and.
- The limit and the function must have equal values at that point.

## How do you check a function is continuous or not?

Saying a function f is continuous when **xc is the same as saying that the function’s two-side limit at xc exists and is equal to f(c).**

## What are the 3 types of discontinuity?

There are three types of discontinuities: **Removable, Jump and Infinite.**

## What are the three steps to determine if a function is continuous?

There are three types of discontinuities: **Removable, Jump and Infinite.**

## What are the continuity theorems?

**If a function f is continuous at x a then we must have the following three conditions.**

- f(a) is defined; in other words, a is in the domain of f.
- The limit. must exist.
- The two numbers in 1. and 2., f(a) and L, must be equal.

## What is the concept of continuity?

In short: **the sum, difference, constant multiple, product and quotient of continuous functions are continuous. Theorem: If f(x) is continuous at xb, and if limxag(x)b, then limxaf(g(x))f(b). In short: the composition of continuous functions is continuous.**