So if we approach by any sequence of points in , say with ,  then we would like sequences of  values of  at to converge to the same value, namely , i.e., . In that case we can predict the value  for at the point  .
Let us look at some examples.

i) Consider a function defined as : 
                                       

                                              
Clearly,  is defined at all points near . Though is defined at  also, our aim is to predict a suitable value for at  by analyzing its values at points near . For example, let us approach the point  by a sequence, i.e., consider any sequence   of points in the domain of  such that for all and . Then, . Since , it follows, from the limit theorems of sequences (see section 3.2.1), that . Hence, we can say that the natural value that  should take at  is 3 .

Click here to see an interactive visualization: Applet 2.1