Tangent Planes and Linear Approximation in 2 Variables

One of the key concepts of calculus is that of linear approximation and local linearity.  Roughly, this says that at any function nice enough to be used in a standard calculus class, if we zoom in far enough, the tangent plane gives a good approximation of the function.  With any concept in multivariable calculus, it is worthwhile to review the same concept, linear approximation, in single variable calculus.

Things to notice:

A worksheet on using the tangent plane to understand local linearity is available.

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.

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Last updated By Mike May, S.J. ,  October 6, 2006.