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Re: need a hand ordering functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16676] Re: [mg16566] need a hand ordering functions
  • From: BobHanlon at aol.com
  • Date: Fri, 19 Mar 1999 12:54:24 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 3/18/99 9:27:53 AM, money00 at angelfire.com writes:

>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.
>

Needs["Graphics`Graphics`"];
Needs["Graphics`Legend`"];

I have assumed that when you wrote n^1+a that you meant n^(1+a).

funcs = { n*Log[n], n^8,n^(1+a), (1+a)^n, 
			n^2 / Log[n], (n^2 - n + 1)^4};

You can investigate the plots of the functions

ShowLegend[LogPlot[Evaluate[funcs /. a -> .5], {n, 1.25, 3}, 
		PlotStyle -> Table[Hue[h], {h, 0, 1, 1/6}], 
		DisplayFunction -> Identity], 
		{Hue[5#/6]&, 6, "1","6", LegendPosition -> {1.1, -.4}}];

Alternatively, you can investigate the series expansions in n

Collect[Expand[Normal[Series[#, {n, 2., 8}]]]& /@ (funcs /. a->.5), n]//
  ColumnForm

Bob Hanlon


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