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 .
We use Eubacteria to produce drugs, wine, and cheese. many eubacteria form spores, resistant to dehydration and most temperatures, when there is no food and can last up to 50 years. all eubacteria are either spirilla (spiral shaped), bacilli (rod shaped), or cocci (spherical). Eubacteria are usually divided into five phylums: Spirochetes, Chlamydias, Gram-positive bacteria, Cyanobacteria (formerly blue-green algae), and Proteobacteria. There are many types of bacteria, many of which are extremely similar, so you may see other groupings.