Limit Function

The notion of limit is very intimately related to the intuitive idea of nearness or closeness. limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Informally, a function f assigns an output f(x) to every input x. The function has a limit L at an input p if f(x) is "close" to L whenever x is "close" to p. In other words, f(x) becomes closer and closer to L as x moves closer and closer to p. More specifically, when f is applied to each input sufficiently close to p, the result is an output value that is arbitrarily close to L. If the inputs "close" to p are taken to values that are very different, the limit is said to not exist.

Degree of such closeness cannot be described cannot be described in terms of basic algebraic operations of addition or subtraction and multiplication and their inverse operations subtraction and division respectively. It comes into play in situations where one quantity depends on another varying quantity and we have to know the behavior of the first when the second is very close to a fixed given value.

In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives and integrals.

Limits are a mathematical tool which is used to define the 'limiting value' of a function i.e. the value a function seems to approach when it's argument(s) approach a particular value. Although, the argument of the function can be taken to approach any value, limits are helpful in cases where the argument approaches a value where the function is not defined or becomes exceedingly large