Marc Renault, supported by Shippensburg University made a complete library of applets for Calculus I that are suitable for in-class demonstrations and/or student exploration. He created these applets using GeoGebra software for creating dynamic visualizations of mathematical ideas.

My favorite applet I have used successfully in the classroom was the chain rule applet. It is a dynamic way to demonstrate the chain rule using an *x*-wheel, a *u*-wheel, and a *y*-wheel. You can change the speed of the *x*-wheel, and you can connect the wheels with belts and change their radii. This model is a great exploration of the chain rule and enhances an intuitive understanding of where the formula comes from. The best part is crossing the belts in the applet!

The Intuitive Notion of the Chain Rule

Marc Renault has a library of calculus applets created with Geogebra on his website:

**Other Calculus Applets**

This applet demonstrates the epsilon-delta definition of the limit. (In particular, we are exploring whether lim f(x)=L as x approaches c)

Epsilon Delta Definition of the Limit