Definition+&+Description+-+Version+2

** Good Job Eduardo and Bertha... [[image:christmastree.gif]] **__ **Limits of functions** __
I. __Definition__

The limit of a function, describes the behavior of a function near a particular input, in other words the limit of f(x) ** ( ** it ** not necessary) **is equal to "L" when "x" approaches "b", if you can find a "x" sufficiently close to "b" such that the value of f(x) is as close to "L" as desired.



A formal definition is, given a function f(x), it is said that it has limit equal to "L" when "x" tends to "b" if for everything ** every **épsilon positive e xists ** there is **a delta (a real number) also positive such that for the module of the distance from "x" up to "b" between 0 and delta happens that ** not necessary **the module of the difference of f(x) minus L is minor that epsilon.

II. __Description__

Properties:
 * If the limit of a function exists that limit is unique.


 * Limit of the sum/subtraction is the sum/subtraction of the limits, it means that the limit when "x" approaches "b" of f(X) plus or minus g(x) it is equal to the limit when "x" approaches "b" of f(X) plus or minus the limit when "x" approaches "b" of g(X).






 * Limit of the multiplication is the multiplication of the limits, it means that the limit when "x" approaches "b" of f(X) times g(x) it is equal to the limit when "x" approaches "b" of f(X) times the limit when "x" approaches "b" of g(X).


 * If g(x) is different of zero, then the limit of the division is the division of the limits, it means that the limit when "x" approaches "b" of f(X) divided by g(x) it is equal to the limit when "x" approaches "b" of f(X) divided by the limit when "x" approaches "b" of g(X).


 * For "k" constant, the limit when "x" approaches"b" of f(X) times "k" it is equal to "k" times the limit when "x" approaches "b" of f(X).


 * The limit when "x" approaches "b" of the nth root of f (x) is equal to the nth root of the limit when "x" approaches "b" of f (x).

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