l'hospitals rule

Mar 2010
35
0
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
 

Chris L T521

MHF Hall of Fame
May 2008
2,844
2,046
Chicago, IL
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: \(\displaystyle e^t=\frac{1}{e^{-t}}\)...
 
Mar 2010
35
0
is there an explanation or proof? or do i just have to memorize this.

thank youu
 

Chris L T521

MHF Hall of Fame
May 2008
2,844
2,046
Chicago, IL
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 \(\displaystyle e^te^{-t}=e^{t-t}=e^0=1\). 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?