What This Document Is
This is a set of lecture notes from a Calculus II course (MATH 231) at the University of Illinois at Urbana-Champaign, specifically Lecture 03B from the Fall 2013 semester. It focuses on the concept of limits, extending the foundational understanding of limits to encompass behavior as variables approach infinity. The material builds upon previously established limit principles and applies them to analyze functions in new contexts.
Why This Document Matters
These notes are invaluable for students currently enrolled in a Calculus II course, or those reviewing the topic of limits at infinity. It’s particularly helpful when tackling problems involving the long-term behavior of functions, and understanding how functions behave with extremely large or small inputs. Students preparing for exams or quizzes covering these concepts will find this resource beneficial for solidifying their understanding. It’s best used *in conjunction* with textbook readings and classroom lectures to reinforce learning.
Topics Covered
* Limits as variables approach infinity
* Determining horizontal asymptotes of functions
* Application of limit principles to functions with infinite limits
* Analyzing the rate of decay of functions
* Connections between exponential and polynomial functions in the context of limits
* Graphical interpretation of limits at infinity
What This Document Provides
* A focused exploration of limits at infinity, building on core calculus concepts.
* A structured presentation of the theoretical framework for evaluating these types of limits.
* Illustrative examples designed to demonstrate the application of limit principles.
* A foundation for understanding asymptotic behavior of functions.
* A resource to support independent study and problem-solving practice.
