Limits at infinity and Horizontal Asymptotes
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.
- Vertical and Horizontal Asymptotes - Practice with Vertical and Horizontal Asymptotes.
- Vertical Tangents; Vertical Cusps - Practice with Vertical Tangents; Vertical Cusps.
- How do you find the limit of a function a infinity?
- What is a horizontal asymptote?
- How do you find the horizontal asymptote of a function?
- What is a rightward horizontal asymptote or leftward horizontal asymptote?
- How can you find horizontal asymptotes by looking at a graph?
- How can you find horizontal asymptotes without looking at a graph?
- How do you find end behavior of a graph?
- How do you calculate the limit of a function as x goes to infinity or negative infinity?
- What is the horizontal asymptote in general for rational functions?
- How do you find the limit at positive infinity and negative infinity for irrational functions?
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Staff Review
Limits of functions are discussed as a x approaches infinity or negative infinity. Some examples are used to help this concept make more sense. You will be able to see in this video how to find these by looking at graphs as well as by analyzing the function itself and looking at what happens when x gets really large positive or negative. A very useful result is obtained on page 7 when we learn what the end behavior is for a rational function given m (degree of numerator) and n (degree of denominator).
