Interactive Demo
The Derivative as a Limit
The Derivative as a Limit is a free, interactive learning demo from the Calculus I: Single Variable Calculus course on Lykke. It helps you build intuition for Differentiation, Rates of Change, Tangent Lines, Derivatives. Play with it directly in your browser — it features 2 sliders and a live visual canvas. This demo lives in the “Part 1: Differentiation” section of the course.
How to use this demo
- Drag the “Interval Δx (h)”, “Point x” sliders to change the inputs and watch the result update live.
- Experiment freely — there's nothing to break, and every change is reversible.
What you'll explore
- Differentiation
- Rates of Change
- Tangent Lines
- Derivatives
Frequently asked questions
What does the The Derivative as a Limit demo do?
The Derivative as a Limit Interval Δx (h) Point x h = 2.00 As h → 0, the secant line (red) approaches the tangent line (green). The Derivative as a Limit lets you explore this hands-on instead of only reading about it.
What Calculus I: Single Variable Calculus concept does The Derivative as a Limit teach?
Explores the mathematical notation, physical meaning, and geometric interpretation of derivatives. It focuses on Differentiation, Rates of Change, Tangent Lines, Derivatives from the “Part 1: Differentiation” section.
What can I control in The Derivative as a Limit?
The “Interval Δx (h)”, “Point x” sliders change the key inputs. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.
How does The Derivative as a Limit fit into the Calculus I: Single Variable Calculus course?
Calculus I: Single Variable Calculus is a comprehensive three-part series designed to bridge the gap between abstract mathematical notation and real-world applications. Led by Professor Gigliola Staffilani of MIT, the c… This demo is the interactive piece for the “Part 1: Differentiation” section. Open the full Calculus I: Single Variable Calculus course wiki at https://www.getlykke.com/explore/public/calculus-i-single-variable-calculus-9ac12726-58e8-4d0b-8a4f-75a32b2484bc for notes, flashcards, quizzes and the other demos.
What will I understand better after using The Derivative as a Limit?
You'll build intuition for Differentiation, Rates of Change, Tangent Lines, Derivatives — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on Calculus I: Single Variable Calculus alone.
From the Calculus I: Single Variable Calculus course
This interactive demo is part of the Part 1: Differentiation section. Explore the full Calculus I: Single Variable Calculus course wiki on Lykke — with notes, flashcards, quizzes and more interactive demos.
Open the Calculus I: Single Variable Calculus course →