The Epsilon-Delta Challenge

The Epsilon-Delta Challenge Epsilon-Delta Game Can you find a δ that keeps the function inside the ε target? The Epsilon-Delta Challenge lets you explore this hands-on instead of only reading about it.

Unit 1 establishes the concept of a limit, which is the cornerstone of calculus. Students learn to evaluate limits using various methods and use limits to define and test for continuity. It focuses on Defining Limits and Limit Notation, Estimating Limits from Graphs and Tables, Algebraic Properties of Limits, Limits at Infinity and Horizontal Asymptotes, Defining Continuity at a Point, The Intermediate Value Theorem (IVT) from the “Unit 1: Limits and Continuity” section.

The “Smooth”, “Hole”, “Jump” buttons run actions or reset the demo. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.

AP Calculus AB is a college-level course that explores the concepts of limits, derivatives, and integrals. Students learn to approach mathematical problems through multiple representations—graphical, numerical, analytic… This demo is the interactive piece for the “Unit 1: Limits and Continuity” section. Open the full AP Calculus AB course wiki at https://www.getlykke.com/explore/public/ap-calculus-ab-c14bedc7-55ee-4bd3-99ff-a9a537a06a66 for notes, flashcards, quizzes and the other demos.

You'll build intuition for Defining Limits and Limit Notation, Estimating Limits from Graphs and Tables, Algebraic Properties of Limits, Limits at Infinity and Horizontal Asymptotes, Defining Continuity at a Point, The Intermediate Value Theorem (IVT) — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on AP Calculus AB alone.