Local Linearity 3D Applet Worksheet

This worksheet is designed to build familiarity with the use of the tangent plane as a linear approximation of a function.  This can be done with the applet obtained by following either of the following links:
http://www.slu.edu/classes/maymk/banchoff/LocalLinearity3d.html
Spread windows where you can see them all.  Increase the size of the control panel so that you can see all the readout boxes.

1) The applet opens with the default function f(x,y)=sin(x*y) centered at the point (2, .5) with del set at 1.

2) Linear approximation is most useful when we have a point P0=(x0,y) and a function f, where f and both of its partials are easy to compute at P0, and we are really interested in f(P1) where P1 is close to P0.

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Last updated By Mike May, S.J., September 23, 2006.