## What is the limit of a function

The limit of a function is used to describe its behaviour when approaches infinity (or some other value). The mathematical notation for the limit of function when approaches is:

### Example

Consider the function . We want to find the behaviour of the function as it approaches the pole (). This is interesting because in this case the denominator of the fraction becomes zero, so is not defined. But how does the function behave when it approaches from a value larger than and from a value smaller than ?

In the case of approaching from above (), we write:

In the case of approaching from below (), we write:

The following graph shows the behaviour:

**Manipulation Rules**

(1)