# Limit

A value of a function as the value of input approaches some value is called limit.

## Introduction

A function gives a value for every input. The value of the function is called the limit when the input closer to some value. In calculus, the concept of limit is used to know the behavior of a function when the input value close to a certain value.

### Representation

$x$ is a variable. A function is formed in terms of $x$ and it is written as $f{(x)}$ mathematically. The function $f{(x)}$ gives a value for every value of $x$. If $x = a$ then the value of function is $f{(a)}$.

Remember, the limit is not the value of function $f{(x)}$ when $x = a$, and it is a value of the function when the value of $x$ closer to $a$. The closer in calculus is denoted by symbol $\to$. Therefore, $x$ closer to $a$ is denoted by $x \to a$. It is read as $x$ tends to $a$ or $x$ approaches $a$.

In calculus, limit is symbolically represented by $\lim$. The limit of $f{(x)}$ is written as $\lim f{(x)}$ but the limit of function is calculated when $x$ approaches $a$. considering all factors, the limit of function $f{(x)}$ when $x$ tends to $a$ is written in mathematically as follows.

$\large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

Take the limit of function $f{(x)}$ is equal to $L$ when $x$ approaches $a$.

$L \,=\, \large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

### Rules

Learn list of formulas of limits with proofs and their use in calculus.