Limits at Infinity | Calculus Lesson 7 – JK Math

How to Evaluate Limits at Infinity (Calculus Lesson 7)

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In this lesson we learn how to evaluate limits at infinity. We learn the basic rules for evaluating limits at infinity, as well as a special limit that can be used to evaluate more complex limits at infinity. This results in us learning the guidelines for quickly evaluating limits at infinity for rational functions based on the powers of x in the numerators and denominators. Also, we learn how a limit at infinity of a function can give us the location of horizontal asymptotes for that function. And finally, we discuss how to deal with limits at infinity of rational functions containing square roots that have two horizontal asymptotes.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes!

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 What is a Limit at Infinity?
0:51 Basic Rules for Limits at Infinity
3:28 Limit at Infinity for a Rational Function (New Special Limits)
6:47 Highest Degree of Numerator Less Than Denominator
10:36 Highest Degree of Numerator Greater Than Denominator
12:08 Three Guidelines for Limits at Infinity of Rational Functions
13:43 Horizontal Asymptotes
14:42 Limit of Rational Function with a Square Root of x^2 at Infinity
16:42 Two Horizontal Asymptotes & Negative Infinity

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