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 > > > > >