What is the limit of a function

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

    equation

Example

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

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

    equation

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

    equation

The following graph shows the behaviour:

limitfunc

Manipulation Rules

(1)   equation