If a variable takes values which are more and more close to a finite number , then we say that approaches written as ).

- If values of come closer to but are always greater than , then we say that approaches form right ().
- If values of come closer to but are always less than , then approaches from left () .

The concept of a **limit** is essentially what separates the field of calculus, and analysis in general, from other fields of mathematics such as geometry or algebra.

The concept of a limit may apply to:

## Contents

## Examples

If , then can approach to '2' from two sides:

**From right side:**In notation we write means is coming closer to '2' from right i.e. it is more than '2'.

**From left side:**In notation we write mean is coming closer to 2 from left i.e. it is less than '2'.

## Meaning of a limiting value

Let be function of . If the expression comes close to as approaches then we say that is the limit of as approaches .

In notation, it is written as .

## Right Hand Limit

If approaches as approaches from the right, then is called as the right hand limit of .

Right hand limit can be expressed in two ways:-

## Left Hand Limit

If approaches from the left, then is called the left hand limit of . The left hand limit can be expressed in two ways:-

**Note that is a positive real number, that we let approach 0.**.

## Existence of Limit

For existence of limit at

### Illustrating the concept

If , then evaluate .

L.H.L. = i.e. is coming closer to 2 but it is less than '2'. So, observe the situation in table below:

1.9 | 0.1 | 3.9 |

1.99 | 0.01 | 3.99 |

1.999 | 0.001 | 3.999 |

Coming closer to 2 but less than 2 | Coming closer to 4 but less than 4 |