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 .
For references see Tangent line.
Tangent plane. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Tangent_plane&oldid=14114