Login

tommy1729 · 08/11/2013, 02:16 AM

Let x-> oo
Let lim f(x)/g(x) = 1.
Let lim f(x)-g(x) does not exist.
Let f(x),g(x) be strictly rising.

What is the min value r such that

1) 0<r<1
2)lim ln^[r](f(x)) - ln^[r](g(x)) exists

(^[] is composition)

regards

tommy1729

tommy1729 · 09/23/2013, 09:24 PM

This question is solved.

Login
Username:
Password:	Lost Password?
	Remember me

Possibly Related Threads...
Thread		Author	Replies	Views	Last Post
	b^b^x with base 0<b<e^-e have three real fixpoints	Gottfried	1	2,017	11/07/2017, 11:06 AM Last Post: sheldonison
	2 real fixpoints again .......	tommy1729	10	8,177	02/23/2016, 10:17 PM Last Post: tommy1729
	Dangerous limits ... Tommy's limit paradox	tommy1729	0	1,731	11/27/2015, 12:36 AM Last Post: tommy1729
	A new set of numbers is necessary to extend tetration to real exponents.	marraco	7	8,395	03/19/2015, 10:45 PM Last Post: marraco
	Real-analytic tetration uniqueness criterion?	mike3	25	19,399	06/15/2014, 10:17 PM Last Post: tommy1729
	Real and complex behaviour of the base change function (was: The "cheta" function)	bo198214	39	47,722	08/13/2011, 06:33 PM Last Post: bo198214
	Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))	Gottfried	91	84,655	03/03/2011, 03:16 PM Last Post: Gottfried
	Tetration Extension to Real Heights	chobe	3	5,761	05/15/2010, 01:39 AM Last Post: bo198214
	1960s stuff on extending tetration to real height?	mike3	7	9,538	03/25/2010, 08:58 PM Last Post: mike3
	b^^y, b<1 and y<-2 to evaluate to the real number!??	nuninho1980	1	2,941	03/23/2010, 10:59 AM Last Post: bo198214