Let f(x) be a function of x. Let a and l be constants such that as , as we have
.
In such case we say that the limit of the function f(x) as x approaches a is l. we write this as



In case , no such number l exist, then we say that does not exist finitely.

Illustration

Let a regular polygon of n sides be inscribed in a circle. The area of the polygon cannot be greater than the area of the circle., however large the number of sides of the polygon increases indefinitely the area of the polygon continually approaches the area of the circle. Thus the difference between the area of the circle and the polygon can be made as small as we please by sufficiently increasing the number of sides of the polygon.

We have ,

(Area of the polygon of n sides)=Area of the circle