Re: Limit without L'Hospital

Hi!

How do you solve without using L'Hospital:

lim{x->oo} ( (e^(1/x) - e^(1/(x+1)) )/(1/(3*x^2) )

?

Best Regards,
Andrew

Little-oh




In article <1141605608.879843.145300@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Andrew" <scootertuner@xxxxxxx> wrote:

Hello Virgil!

Can you be more explicit?

Andrew

As x -> +oo, one has
e^(1/x) = 1 + 1/x + + o(1/x)
e^(1/(x+1)) = 1 + 1/(x+1) + + o(1/x)
where o(f(x)) is a term which goes to zero more rapidly than f(x), so
(e^(1/x) - e^(1/(x+1)) )/(1/(3*x^2) = 3*x/(x+1) + o(1)
.