If the curve of -plane is sufficiently smooth in its point and in a neighborhood of this, the curve may have a tangent line (or simply ) in . Then the tangent line of the curve in the point is the limit position of the secant line through the two points and of the curve, when limitlessly tends to the value (i.e. . Due to the smoothness,
and the slope of the secant (http://planetmath.org/SecantLine) tends to
which will be the slope of the tangent line.
Note. Because the tangency is a local property on the curve, the tangent with the tangency point may intersect the curve in another point, and then the tangent is a secant (http://planetmath.org/SecantLine), too. For example, the curve has the line as its tangent in the point but this line the curve also in the point .
|Date of creation||2013-03-22 14:50:31|
|Last modified on||2013-03-22 14:50:31|
|Last modified by||Mathprof (13753)|
|Synonym||tangent of the curve|
|Synonym||tangent to the curve|