The derivative of a function evaluated at a point gives the slope of one of these lines at that point.
A space named for this term is the dual of the quotient of the maximal ideal of a local ring and the product of maximal ideals, and is named for Zariski. An n-dimensional compact manifold with a copy of R-n at a point with this relationship to the point is this type of space at that point. A curve's curvature is defined as the magnitude of the rate of change of a unit vector of this type with respect to arc length. In linearization, the value of a function at a point is approximated by calculating its value on this type of plane. The derivative of a function evaluated at a point gives the slope of one of these lines at that point. This term names a trigonometric function equal to sine divided by cosine. For 10 points, name this type of line that touches a circle at exactly one point.
A space named for this term is the dual of the quotient of the maximal ideal of a local ring and the product of maximal ideals, and is named for Zariski.
tangent [or cotangent until "relationship" is read]