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This applet allows the user to look at the Taylor polynomial approximation to a function \(f(x)\).

Set eccentricity and watch the planet move around. Illustrates Kepler's second law by clearly showing how velocity varies at different points of an elliptical orbit.
This applet is designed to build the intuition between the idea of a derivative being the slope of the line tangent to a curve and the idea of a derivative as a function symbolically computed from
Graphs of the brachistochrone curve, including an animation of a "race" along it and other curves, and much historical background.
Alphabetical list of well-known curves from Apple of Discord (Cycloid) and Astroid to Wankel's Engine (Reuleaux Polygons) and Witch of Agnesi, with graphs, equations, interesting facts, and histor
Leibniz: First Published Rules for the Derivative: Images of the first appearances of the Product and Quotient Rules in print in an article by Leibniz in a 1684 issue of the journal Acta Eruditoru

The expression \(0^0\) is usually called an indeterminate form.

A summary of the history of the problem of finding the region of greatest area bounded by a given perimeter, from Zenodorus and Pappus to Jakob Steiner (one page each).