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A way to organize functions by their speed of growth ?

  1. May 25, 2009 #1
    A way to organize functions by their "speed of growth"?

    How does one say formally in math that a certain function grows "faster" than another?
    Doens't really work for trig functions, i know.
    you knotice that the exponential function is the function dividing d/dx slower than itself and d/dx faster than itself functions

    In order from slower to faster:

    Derivative is slower than itself:
    Constants

    rational function in which quotient is non-constant

    Logarithms

    Roots

    Non-constant polynomials:

    b^x, b>1: derivative is proportional to itself

    Derivative is faster than itself:

    Self-power:x^x

    Gamma(x)

    Tetrational function [tex]{}^xb=b[4]x[/tex]; b[4]1=b, b[4]2=b^b, b[4]3=b^(b^b), etc. (note the grouping)
     
    Last edited: May 25, 2009
  2. jcsd
  3. May 25, 2009 #2
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