Re: uniqueness of limits at infinity

From: GEIvey (George.Ivey_at_gallaudet.edu)
Date: 09/20/04 

Date: Mon, 20 Sep 2004 13:27:41 +0000 (UTC)

On 20 Sep 2004, Jani Yusef wrote:
>X-No-archive: yes
>Is it true that for some two functions f(n) and g(n) that as n
>approaches infinity f(n)/g(n) has a unique limit?
>I believe the answer is yes but is this true? Is their a specific
>theorem which demonstrates this? I don't need aproof of this, I'd just
>liek my suspicion confirmed/denied.
>Thanks!!

   Your question is not clear. If f(n)/g(n) HAS a limit then that limit is unique- that's true of all limits. If f and g HAVE limits AND the limit of g is not 0, then the limit f(n)/g(n) exists: and is
(lim f(n))/(lim g(n)). If f and g HAVE limits but the limit of g is 0, then lim f(n)/g(n) may or may not exist. Similarly, if f and g do NOT have limits, lim f(n)/g(n) may or may not exist.