## University Calculus: Early Transcendentals (3rd Edition)

$f(t)$, $g(t)$ and $h(t)$ are continuous at $t=t_0$ so, $r(t)$ is also continuous at $t=t_0$
Since, $r(t)=\lt f(t), g(t), h(t) \gt$ or, $r(t)=\lt f'(t), g'(t), h'(t) \gt$ Since $r'(t)$ is differentiable at $t=t_0$ thus, $f(t)$, $g(t)$, and $h(t)$ are also differentiable at $t=t_0$ Hence, $f(t)$, $g(t)$, and $h(t)$ are continuous at $t=t_0$ so, $r(t)$ is also continuous at $t=t_0$