Let be a positive integer greater than 1. A function from a subset of to the Cartesian product is called a vector-valued function of one real variable. Such a function to any real number of a coordinate vector
Example. The ellipse
is the value set of a vector-valued function ( is the eccentric anomaly).
Example. If is continuous on , the set
is a (continuous) curve in . It follows from the above definition of the derivative that is the limit of the expression
as . Geometrically, the vector (3) is parallel to the line segment connecting (the end points of the position vectors of) the points and . If is differentiable in , the direction of this line segment then tends infinitely the direction of the tangent line of in the point . Accordingly, the direction of the tangent line is determined by the derivative vector .
|Date of creation||2013-03-22 19:02:19|
|Last modified on||2013-03-22 19:02:19|
|Last modified by||pahio (2872)|