Limits of Parametric Curves

Tip: Limits of Parametric Curves

Let $\gamma :I\subseteq \mathbb{R}\to {\mathbb{R}}^n$ be a Parametric Curve and let $t_0$ be an Accumulation Point of $I$.

Then $\mathbf{L}\in {\mathbb{R}}^n$ is the limit of $\gamma$ for $t\to t_0$ if and only if for each $\epsilon >0$, there exists some $\delta >0$ such that for all $t\in I$

$$0<||t-t_0||<\delta ⟹||\gamma (t)-\mathbf{L}||<\epsilon$$