continuous function

Continuous Functions §

A continuous function is a function that does not have any gaps or jumps in its graph. In other words, the function is continuous if it can be drawn without lifting the pen from the paper.

Mathematically, a function $f(x)$ is continuous at a point $a$ if the limit of $f(x)$ as $x$ approaches $a$ is equal to $f(a)$.

In symbolic form, it can be represented as:

${\lim }_{x\to a}f(x)=f(a)$

Understanding the concept of continuity is crucial in calculus and real analysis, as it helps in understanding the properties and behaviours of different types of functions.