Answer
$\lim\limits_{t \to t_0} f(t)=f(t_0)$; $\lim\limits_{t \to t_0} g(t)=g(t_0)$ and $\lim\limits_{t \to t_0} h(t)=h(t_0)$
$f$, $g$, and $h$ are continuous at $t=t_0$
Work Step by Step
Since, $\lim\limits_{t \to t_0}r(t)=\lt f(t), g(t), h(t) \gt$
Since $r(t)$ is continuous at $t=t_0$ thus, $\lim\limits_{t \to t_0}r(t)=r(t_0)=\lt f(t_0), g(t_0), h(t_0) \gt$
Thus, we have $\lim\limits_{t \to t_0} f(t)=f(t_0)$; $\lim\limits_{t \to t_0} g(t)=g(t_0)$ and $\lim\limits_{t \to t_0} h(t)=h(t_0)$
We see that $f$, $g$, and $h$ are continuous at $t=t_0$
