Rational Functions provides us with the most incredible example of Limits at Infinity!
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Before we get ahead of ourselves, let’s first talk about what a Limit is.
A limit describes what is happening to the function as we approach a certain number. Limits are the building blocks for everything we will see in calculus: continuity and differentiability, derivatives and integrals.
The concept of “getting closer to” without touching, is the main idea behind limits and is beautifully displayed in all rational functions.
Think about asymptotes… they represent numbers that we can only approach but never touch.
Using limits to find End Behavior of Rational Functions
Together, we will look at two types of Limits as they pertain to Rational Functions:
- Limits Involving Infinity
- Limits at Infinity
What’s the difference?
Well, Limits Involving Infinity is when our answers will be either positive or negative infinity. This happens when we are approaching a Vertical Asymptote from either the left-hand side or the right-hand side.
Limits at Infinity helps us to describe our end behavior and gives us a big picture of our functions true asymptotic behavior. More importantly, it gives us a formal definition for finding Horizontal Asymptotes, as Paul’s Online Notes so rightly states.
Together we will look at both types and see how Rational Functions play a significant role in understanding Calculus.
Rational Functions in Calculus – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.