What This Document Is
This document comprises complete course notes for Emory University’s Calculus I (MATH 111) course. It’s a consolidated resource covering fundamental concepts and techniques related to limits and continuity – the foundational building blocks of calculus. These notes are designed to serve as a comprehensive companion to lectures and textbook readings.
Why This Document Matters
These notes are essential for students enrolled in MATH 111, providing a structured and detailed record of the course material. They are particularly valuable for review during exam preparation, clarifying challenging concepts, and reinforcing understanding outside of class. Students who struggle with the abstract nature of limits and continuity will find these notes a helpful reference point. The document is most useful when used *alongside* active participation in the course and completion of assigned problem sets.
Common Limitations or Challenges
This document provides a record of concepts, but it does not replace the need for active learning. It won’t teach you *how* to solve problems, nor does it offer practice exercises with solutions. A strong grasp of calculus requires consistent practice and application of the principles outlined within. These notes are a support tool, not a substitute for engagement with the course material.
What This Document Provides
The complete course notes include:
* A detailed explanation of limit laws, including the constant multiple rule, sum/difference rule, power rule, and quotient rule.
* Coverage of the Squeeze Theorem and its application to evaluating limits.
* A thorough discussion of continuity, including definitions of removable and non-removable discontinuities (holes, vertical asymptotes, and jump discontinuities).
* Techniques for analyzing rational functions and identifying potential discontinuities.
* An introduction to the Intermediate Value Theorem and its applications.
* Discussion of the order of vanishing and composite function limits.
* An overview of limits at infinity and horizontal asymptotes.
This preview *does not* include worked examples, practice problems, or detailed proofs of theorems. It focuses on outlining the *topics* covered in the full document.
