Illustration 8 Consider the function ( )

Illustration Consider the function ( ) f x for x > . We want to know x → f ( x ). Here, observe that the domain of the function is given to be all positive real numbers. Hence, when we tabulate the values of f ( x ) , it does not make sense to talk of x approaching from the left. Below we tabulate the values of the function for positive x close to (in this table n denotes any positive integer). From the Table . given below, we see that as x tends to , f ( x ) becomes larger and larger. What we mean here is that the value of f ( x ) may be made larger than any given number. Table . . . – n f ( x ) 10000 n Mathematically, we say f x = +∞ We also remark that we will not come across such limits in this course. Illustration We want to find f x , where , , , f x <    + >  As usual we make a table of x near with f ( x ) . Observe that for negative values of x we need to evaluate x – and for positive values, we need to evaluate x + . Table . From the first three entries of the Table . , we deduce that the value of the function is decreasing to – and hence. f x = − – . – . – . . . . f ( x ) – . – . – . . . . LIMITS AND DERIVATIVES From the last three entires of the table we deduce that the value of the function is increasing from and hence f x Since the left and right hand limits at do not coincide, we say that the limit of the function at does not exist. Graph of this function is given in the Fig13. . Here, we remark that the value of