Chapter 12 - Vector-Valued Functions - 12.1 Exercises - Page 822: 71

\begin{array}{l}{\mathbf{r}(t)}{\text { is continuous on }[-1,1]}\end{array}

Given$$\mathbf{r}(t)=t \ \mathbf{i}+\arcsin t \ \mathbf{j}+(t-1) \mathbf{k}$$ Since we have $-1\leq\sin x \leq1 $, $\arcsin t $ is defined in the interval $[-1,1]$ So, \begin{array}{l}{\mathbf{r}(t)}{\text { is continuous on }[-1,1]}\end{array}