# Limits

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

Limit is a basic mathematical concept for learning calculus and it is useful determine continuity of function and also useful to study the advanced calculus topics derivatives and integrals.

## Basics

There are two basic concepts to understand the concept of limits clearly in calculus.

### 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 $a$.

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

### One sided Limits

Learn how to find the left and right hand limits with understandable examples

### Rules

Learn list of properties and standard results in limits to use them as formulas while evaluating the limit of any function in calculus.

### Methods

The list of methods to learn how to find the limits of functions in calculus with understandable examples and worksheets for practice.

### Problems

List of limits problems with solutions for leaning and practicing.

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