1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Order by asymptotic growth rate

  1. Feb 18, 2012 #1

    dba

    User Avatar

    1. The problem statement, all variables and given/known data
    I try to order given functions and I am stuck with evaluating the following:

    [itex]f(n)= (n+1)![/itex] and [itex]g(n)=n^{logn}[/itex]

    2. Relevant equations
    [itex]\lim_{n\to\infty}\frac{f(n)}{g(n)} = 0 [/itex]

    then g(n) is faster growing.

    [itex]\lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty[/itex]

    then f(n) is faster growing.

    3. The attempt at a solution
    I would guess that [itex]n^{logn}[/itex] is the faster growing function because it is exponential.
    Thus, I write
    [itex]\lim_{n\to\infty}\frac{(n+1)!}{n^{logn}}[/itex] and would expect the result to be zero.

    My problem is that I do not know hot to take the limit of a factorial function and I also have a problem with the n^logn.
    Can someone help me with this? Maybe I can write the functions in a different way?

    Thanks for any help.
     
  2. jcsd
  3. Feb 19, 2012 #2
    Edit: Nevermind. Now I'm curious though.

    [STRIKE]I might just be going out on a limb here, but I think that looking at it from this perspective might help:

    By the definition of logarithm,
    [itex]log_{10}n = x[/itex]
    implies
    [itex]n = 10^x[/itex]

    I hope it helps at least[/STRIKE]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Order by asymptotic growth rate
  1. Asymptotic Notation (Replies: 1)

Loading...