# The concept of Limit.

### What is limit?

First study the following picture:

You can see in the figure ; if a polygon is inscribed inside a circle , then

as we increase the number of sides of polygon the area of polygon gradually increases .

As we increase the number of sides in the polygon it’s area gradually approaches

the area of  circle and if we take a polygon with sufficiently large number of sides in same configuration

then , the area of the polygon will become almost equal to the area of circle  , but

it will never be equal to   the area of the circle.

In this case , the limit or limiting value of the area of polygon when the number of sides in polygon tends to infinity  is the area of circle which encloses it.

mathematically we can denote this case as:

If the number of sides in the polygon is denoted by “n”  , the function which defined the area of polygon is  f(n) and the area of circle which encloses the polygon is denoted by “A” then :

$\displaystyle\lim_{n\to\infty}f(n)=A$

Similarly we can denote this case of limit in any function an example is given below:

If a function is defined by f(x)=x+2

Then if we limit the value of  ”x” to “1″ then the value of the function “f” approaches 1+2=3

Which can be shown as:

$\displaystyle\lim_{x\to1}x+2=3$

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