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Tangent plane

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to a surface at a point

The plane passing through characterized by the property that the distance from this plane to a variable point of as approaches arbitrarily close to is infinitesimally small as compared to the distance . If is given by an equation , then the equation of the tangent plane at a point , where , has the form

if and only if has a total differential at the point . In this case, and are the values of the partial derivatives and at .


Comments

For references see Tangent line.

How to Cite This Entry:
Tangent plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_plane&oldid=31614
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article