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How can I calculate the Asymptotic Rate of growth of a function, for instance like:

$X^3 - X^2 - X -1$

EDIT:

For instance, as you can see in this graph, after the 1200 the function approximates to the limit. I want to if there is a easy way to calculate the rate of grow, after 1200 for instance.

enter image description here

Edit

I'm trying to find a generalized way in order to graphically find it for Fibonacci, Tribonacci, Tetranacci sequences

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1  
Isn't it O(x^3)? – belisarius Oct 8 '12 at 1:06
Are you asking for a generalized way of determining which term, e.g. x^3, x^2, x, or 1 grows fastest as x increases? – Eric Brown Oct 8 '12 at 1:14
For polynomials, this answer or this answer might be what you're looking for. Possible duplicate – rm -rf♦ Oct 8 '12 at 1:17
5  
It doesn't happen all of a sudden at 1200... it's just that the plot range is such that it seems it is that way. As a hint, look at LogPlot[Fibonacci[n], {n, 0, 1500}] – rm -rf♦ Oct 8 '12 at 1:48
1  
All the $n$-nacci sequences have exponential behavior; the base of their dominant exponential term is (expressed in Mathematica notation) Root[x^n - Sum[x^k, {k, 0, n - 1}], Mod[n, 2, 1]]. – J. M.♦ Oct 8 '12 at 3:23
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