Concept of Limit in Mathematics

In mathematics, the limit is a concept that describes the tendency of a succession or a function, as the parameters of that sequence or function approach a particular value. The limit of a function is a fundamental concept of mathematical differential calculus.


Informally, the fact that a function f has a limit l at point P, it means that the value of F could be as close to L as desired, taking points close enough to P, but P. Reds in actual analysis for functions of a variable, one could make a boundary definition similar to that of a succession boundary, in which, the values that the function takes within an interval are approximated to a fixed point C, regardless of whether it belongs to the function domain.

This could be further extended to functions of several variables or functions in ditinted metric spaces. Informally, it is said that the limit of the function f(x) is L when x tends to C and is written:

Concept of Limit

If you can find a x sufficiently close to C for each occasion such that the value of f(x) is as close to L as desired.
For greater mathematical rigour the definition epsilon-delta of limit is used, which is stricter and makes the limit in a great tool of the real analysis. Its definition is as follows:
“The limit of f(x) when x tends to C is equal to L if and only if for all real number ε greater than zero there is a real number δmayor that zero such that if the distance between x and C is less than Δ,” “then the distance between the image of X and L is less than εunidades.”
This definition, can be written using logical-mathematical terms and in a compact way:
concept of limit
If F(x) and g (x) are functions of real variable and k is a scalar, then the following properties or rules are fulfilled.