Section 13.1: Vector Functions and Space Curves

Show that \(\lim_{t \to a} \mathbf{r}(t) = \mathbf{b}\) if and only if for every \(\epsilon > 0\) there is a number \(\delta > 0\) such that if \(0 < |t-a| < \delta\) then \(|\mathbf{r}(t) - \mathbf{b}| < \epsilon\)