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Re: need a hand ordering functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16661] Re: [mg16566] need a hand ordering functions
  • From: Robert Pratt <rpratt at math.unc.edu>
  • Date: Fri, 19 Mar 1999 12:54:08 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Hint: Try comparing them two at a time by computing the limit 
(n->Infinity) of their ratio.

Also, you need parentheses around 1+a in n^(1+a).

Rob Pratt
Department of Mathematics
The University of North Carolina at Chapel Hill
CB# 3250, 331 Phillips Hall
Chapel Hill, NC  27599-3250

rpratt at math.unc.edu

http://www.math.unc.edu/Grads/rpratt/

On Wed, 17 Mar 1999, `WeDge wrote:

> ok, any help with this would be appreciated heaps.
> The problem is, i have have six functions
> 
> 1)  n log n
> 2)  n^8                   (n to the power of eight)
> 3)  n^1+a               (n to the power of one plus a)
> 4)  (1+a)^n             (one plus a to the power of n)
> 5)  n^2 / logn          (n squared over log n)
> 6)  (n^2 - n+1)^4   (n squared minus n plus one to the power of four)
> 
> now using the relations "proper subset" and "equals" i have to put the
> above into a sequence where "a" is the arbitrary real constant, 0<a<1.
> 
> I know that te 4th function is the largest and
> that the 2nd and 6th functions should be the same size
> after that i'm stuck to be honest. If anyone could give me a hand with
> this, I would be really gratefull.
> 
> Thanks
> 
> 
> 
> 
> 



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