This lesson covers limits at positive and negative infinity and horizontal asymptotes. A function has a horizontal asymptote if its graph approaches a horizontal line for large positive or negative x. The line y equals p is a rightward horizontal asymptote if the limit as x approaches infinity of f of x equals p, and a leftward horizontal asymptote if the limit as x approaches minus infinity of f of x equals q. Calculating limits at plus or minus infinity for rational functions involves analyzing the degree of the numerator and denominator. Finally, the lesson notes that limits at infinity may not exist for some functions, including some non-rational functions.
Limits at positive and negative infinity and horizontal asymptotes. Calculation of limits at positive / negative infinity.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.