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!

Little o notation

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Given two functions f and g with derivatives in some interval containing 0, where g is positive. Assume also f(x) = o(g(x)) as x → 0. Prove or disprove each of the following statements:


    a)∫f(t) dt = o(∫g(t)dt) as x → 0 (Both integrals goes from 0 to x)
    b)derivative of f(x) = o( derivative of g(x)) as x → -

    Can any one show me how to prove this? thanks
     
  2. jcsd
  3. Feb 12, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    Recall, ##f = o(g)## implies :

    ##\forall k>0, \exists a \space | \space f(x) < kg(x), \forall x>a## where 'k' and 'a' are arbitrary constants.

    That's what you meant by "Assume also f(x) = o(g(x)) as x → 0" right?
     
  4. Feb 12, 2013 #3
    f=o(g) as x -> 0 means lim f/g ->0 as x ->0
     
  5. Feb 12, 2013 #4

    Zondrina

    User Avatar
    Homework Helper


    Not true, what about f = x2, then x2 = o(x3) ( For example ).

    Then x2/x3 = 1/x → ±∞ as x → 0.
     
  6. Feb 12, 2013 #5
    That is the definition of the little o notation
     
  7. Feb 12, 2013 #6

    Zondrina

    User Avatar
    Homework Helper

    No, the definition is what I've given you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Little o notation
  1. Big O notation (Replies: 1)

  2. Big-O Notation (Replies: 1)

Loading...