Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
Last reviewed:January 2021
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A term describing a relationship of two figures (usually of the same dimension) in the neighborhood of a common point. The figures are tangent at a point P if they touch at P but do not intersect in a sufficiently small neighborhood of P. To be more precise, if P denotes a point of a curve C (see illustration), a line L is a tangent to C at P provided L is the limit of lines joining P to a variable point Q of C, as Q approaches P along C (that is, for Q sufficiently close to P, the line PQ is arbitrarily close to L). If curve C has equation y = f(x) and point P on C has coordinates (x0,y0), it is shown in the calculus that the slope of the line tangent to C at P is the value of the derivative f′(x) for x = x0. See also: Calculus
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