Tangent plane
From Encyclopedia of Mathematics
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. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Tangent_plane&oldid=14114
Tangent plane. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Tangent_plane&oldid=14114
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098