Results 1 to 4 of 4

Thread: Proving that a function is equal to a big O function

  1. #1
    Super Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    734
    Thanks
    2

    Proving that a function is equal to a big O function

    Can someone give me a hint to get me started? Below is the problem. It's proving that a function is equal to a big O function.
    Attached Thumbnails Attached Thumbnails Proving that a function is equal to a big O function-20170207_184155000_ios.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,595
    Thanks
    2359

    Re: Proving that a function is equal to a big O function

    $f \sim \mathcal{O}(g) \Leftrightarrow \exists M >0,x_0 \ni x>x_0 \Rightarrow |f| \leq M|g|$

    here

    $f(n) = 4n^4 + 5n^2 +32$

    $g(n) = n^4$

    we need to find $M>0,~n_0$

    such that

    $n>n_0 \Rightarrow | 4n^4 + 5n^2 +32| \leq M |n^4|$

    everything is positive so we can drop the absolute value signs

    $n>n_0 \Rightarrow (4-M)n^4 + 5n^2 + 32 \leq 0$

    $n_0=1,~M=41$ satisfies this inequality, so does

    $n_0=3,~M=5$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    734
    Thanks
    2

    Re: Proving that a function is equal to a big O function

    So basically if we could find values of n for which f(n) < 0(n^4), then it is true.
    Last edited by asilvester635; Feb 7th 2017 at 11:29 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    734
    Thanks
    2

    Re: Proving that a function is equal to a big O function

    Quote Originally Posted by romsek View Post
    $f \sim \mathcal{O}(g) \Leftrightarrow \exists M >0,x_0 \ni x>x_0 \Rightarrow |f| \leq M|g|$

    here

    $f(n) = 4n^4 + 5n^2 +32$

    $g(n) = n^4$

    we need to find $M>0,~n_0$

    such that

    $n>n_0 \Rightarrow | 4n^4 + 5n^2 +32| \leq M |n^4|$

    everything is positive so we can drop the absolute value signs

    $n>n_0 \Rightarrow (4-M)n^4 + 5n^2 + 32 \leq 0$

    $n_0=1,~M=41$ satisfies this inequality, so does

    $n_0=3,~M=5$
    That is a little too advanced for me. Here is what I got. Check it out.
    Attached Thumbnails Attached Thumbnails Proving that a function is equal to a big O function-20170207_203248000_ios.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proving a function is a one to one function
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: Aug 1st 2015, 05:36 PM
  2. Replies: 2
    Last Post: May 2nd 2013, 03:19 AM
  3. Derivative of trig function to equal zero.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 1st 2013, 09:15 PM
  4. Replies: 4
    Last Post: Nov 5th 2009, 12:53 PM
  5. Trigonometric function equal to one another
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Feb 14th 2009, 03:48 PM

/mathhelpforum @mathhelpforum