how does
lim t*e^t
t--> - infinity
=
lim t/e^-t
t--> - infinity
how does the e^t turn into e^-t in the denominator??
THANKS
You can think of it this way. Observe that $\displaystyle e^te^{-t}=e^{t-t}=e^0=1$. Thus, we see that either $\displaystyle e^te^{-t}=1\implies e^{-t}=\frac{1}{e^t}$ or $\displaystyle e^{t}=\frac{1}{e^{-t}}$. In our case, we want the latter result.
Does this clarify things a little bit?