Previous Next

Intuition can usually lead to the right answer with these problems, but the following is a more methodical way of calculating limits at infinity.

Evaluating Limits at Infinity

In order to find horizontal asymptotes, we must evaluate limits as x approaches infinity. To evaluate the limits of rational functions at infinity, first divide each of the terms in the numerator and the denominator by the highest. For example, to evaluate

   

first divide each of the terms in the numerator and denominator by the highest power of x present in the function. In this case, that is x3.

   

then evaluate the individual limits using the following rule: if r is a rational number greater than zero such that xr is defined for all x, then

= 0    

Applying this rule in this case leads to the following:

=    

Previous page Vertical and Horizontal Asymptotes page 1 Next section

Take a Study Break