Calculate the value $-te^{-t} - e^{-t}$ at t $\rightarrow\infty$ I am trying to evaluate the following equation at $t \rightarrow \infty$ and $t \rightarrow 0$: 
$-te^{-t} - e^{-t}$ 
I am trying to use L'Hopital's Rule to evaluate $-te^{-t}$ at $\infty$, so it becomes $\frac{e^{-t}}{-t^{-1}}$, but it does not work for me. Any help?

Try this:
$$-te^{-t}-e^{-t}=\frac{-t-1}{e^t}$$
Using l'hospitals
$$\frac{-1}{e^t}\to 0$$
Note that at $t=0$ we don't need l'hospitals. We simply get $\frac{-1}{1}=-1$
