Calculate the value $-te^{-t} - e^{-t}$ at t $\rightarrow\infty$

Question

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?

Do you perhaps mean limit? Because $t=\infty$ makes no sense. — , Jan 09 '16 at 06:50

score 0 · Accepted Answer · answered Jan 09 '16 at 06:51

0

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 $\frac{-1}{1}=-1$

answered Jan 09 '16 at 06:51

pancini

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Calculate the value $-te^{-t} - e^{-t}$ at t $\rightarrow\infty$

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