Definition:Limit of Vector-Valued Function/Definition 1

Definition
Let:
 * $\mathbf r: t \mapsto \begin {bmatrix} \map {f_1} t \\ \map {f_2} t \\ \vdots \\ \map {f_n} t \end {bmatrix}$

be a vector-valued function.

The limit of $\mathbf r$ as $t$ approaches $c$ is defined as follows:

where each $\lim$ on the is a limit of a real function.

The limit is defined to exist precisely when all the respective limits of the component functions exist.

Also see

 * Equivalence of Definitions of Limit of Vector-Valued Function