Illustration 8 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 = − – . – . – .