1. ## l'hospitals rule

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

2. Originally Posted by calculus0
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
Its a rule of exponents: $e^t=\frac{1}{e^{-t}}$...

3. is there an explanation or proof? or do i just have to memorize this.

thank youu

4. Originally Posted by calculus0
is there an explanation or proof? or do i just have to memorize this.

thank youu
You can think of it this way. Observe that $e^te^{-t}=e^{t-t}=e^0=1$. Thus, we see that either $e^te^{-t}=1\implies e^{-t}=\frac{1}{e^t}$ or $e^{t}=\frac{1}{e^{-t}}$. In our case, we want the latter result.

Does this clarify things a little bit?

5. OHH. ok. makes perfect sense!!

thankss