Linear approximation
Animations
Animation: A long zooming in of the graph of a function and its tangent line. [Douglas Arnold]
Animation: The same animation in split screen, tallying the difference between the values of the function and the tangent line. [Douglas Arnold]
Applets
Affine approximations: Mess around with the slope of a line passing through a point to convince yourself that the tangent slope is the best approximation near the point. [Dan Sloughter]
Linear approximations applet: Another applet designed to do the same, but this one lets you vary the base point and slide the slope. [Dartmouth]