Evaluate the limit for \( \mathbf{r}(t)=\left\langle t^{-6}, \sin (t),-4\right\rangle \) \[ \lim _{h \rightarrow 0} \frac{\mathbf{r}(t+h)-\mathbf{r}(t)}{h}=\langle f(t), g(t), h(t)\rangle \] (Use subsymbolic notation and fractions where needed.)