Definition of a Tangent Plane We all have and intuitive idea of what the tangent plane to a point on a given surface should be. It is the plane that goes through that point and that it is tangent to the surface at that point. Suppose. z = f(x,y) is a smooth surface above the xy-plane (see the picture below).
The two prokaryotic domains (or empires),  Bacteria  (or  Eubacteria ) and  Archaea  (or  Archaeobacteria ), are subdivided into 35 phyla (or divisions): 30 phyla in the domain  Bacteria , and 5 phyla in the domain  Archaea .
The Eubacteria, also called just bacteria, are one of the three main domains of life, along with the Archaea and the Eukarya. Eubacteria are prokaryotic, meaning their cells do not have defined, membrane-limited nuclei. As a group they display an impressive range of biochemical diversity, and their numerous members are found in every habitat on Earth.