The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Home Partial Differentiation Implicit Functions Examples Example 6: Tangent Plane
 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

Example 6: Tangent Plane

Find 11_partial_differentiation-397.gif and 11_partial_differentiation-398.gif where

w = x2 + 2y2 + 3z2, z = e5x+y.

11_partial_differentiation-399.gif

Then

11_partial_differentiation-400.gif

The graph of an equation

F(x, y, z) = 0 is a surface in space. The Implicit Function Theorem can be generalized to this case.

11_partial_differentiation-401.gif

Figure 11.6.9

We shall skip the details, but the end result is an equation for the tangent plane of the surface, pictured in Figure 11.6.9.
Home Partial Differentiation Implicit Functions Examples Example 6: Tangent Plane

Last Update: 2006-11-15