Module 1: Limits and Continuity
Welcome to Calculus! In this module you will build the essential foundation: understanding limits intuitively, computing them with algebraic techniques, exploring behavior at infinity, and mastering continuity.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Explain the intuitive concept of a limit using tables and graphs
- Evaluate limits algebraically using direct substitution, factoring, and rationalization
- Determine limits at infinity and identify horizontal and vertical asymptotes
- Define continuity at a point and on an interval
- Apply the Intermediate Value Theorem to locate roots of equations
Module Lessons
The Intuitive Idea of a Limit
Explore what it means for a function to approach a value. Use tables, graphs, and one-sided limits to build intuition.
30-40 minutes
Computing Limits Algebraically
Master the algebraic techniques: direct substitution, factoring, rationalization, and limit laws.
35-45 minutes
Limits at Infinity and Asymptotes
Investigate end behavior, horizontal asymptotes, and infinite limits that produce vertical asymptotes.
30-40 minutes
Continuity and the Intermediate Value Theorem
Learn the formal definition of continuity, identify types of discontinuities, and apply the IVT.
30-40 minutes
After the Lessons
Practice Problems
Apply what you have learned with 10 practice problems covering all module topics. Step-by-step solutions included!
Practice ProblemsModule Quiz
Test your understanding with a 10-question quiz covering limits, limit laws, asymptotes, and continuity.
Take Module QuizStudy Materials
Download printable study guides and quick reference cards for exam prep.