Part 2/6:
\lim_{t \to a} f(t) \
\lim_{t \to a} g(t) \
\lim_{t \to a} h(t)
\end{pmatrix}
]
This definition stipulates that the limits of the component functions must exist for the limit of the vector function to be defined. Thus, the limit of the vector function as ( t ) approaches ( a ) results from combining the limits of its components.
Length and Direction
When we state that
[
\lim_{t \to a} \mathbf{r}(t) = \mathbf{l}
]
we can interpret this to mean that as ( t ) approaches ( a ), the length and direction of the vector ( \mathbf{r}(t) ) converge towards those of another vector ( \mathbf{l} ). In essence, the behavior of the vector can be quantitatively described by considering how close it gets to the vector ( \mathbf{l} ) in terms of both magnitude and direction.