Limits of Trignometric Functions

Limits of Trignometric Functions
The Function : Let A and B be two non empty sets. A function f from A to B denoted by \(f:\,A \to B\)   is a rule that “assigns (or) maps every element of A to an Unique element of B.
Note : In \(f:\,A \to B\), A is called “domain” of the function f and B is called “codomain” of the function f.
    e.g Let  \(A\, = \,\{ 1,2,3\} ,\,\,B = \,\{ p,q,r,s,t\} \)
    Now 
                
    Now 
   \(f:\,A \to B\)  is a function.
Limit of a function : 
Ø Let \(f:\,A \to R\) be defined as f(x)=x+1. Let as observe the behaviour of the function as the variable x approaches (or tends)
to 2.

Ø Here x approaches to 2 means, that it may approaches from left (or) right as follows.
            
                                        
Ø    We observe that as x value approaches to 2 either from left side or right side of f(x),  f(x) value approaches to 3.
Ø    This ‘3’ is called “The Limit” of the function f(x)=x+1, as x  tends to 2.
Ø    This process can be denoted symbolically as follows \(\mathop {Limit}\limits_{x \to 2} \,\,of\,(x + 1)\, = \,3\,\)  (or)  in short \(\mathop {Lt}\limits_{x \to 2} \,\,(x + 1)\, = \,3\,\)