Results 1 to 3 of 3

Math Help - limit

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    limit

    I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

    Thx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by math.link View Post
    I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

    Thx
    -1 \leq \cos x^2 \leq 1...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313
    Quote Originally Posted by math.link View Post
    I need to show that lim[cos(x^2)/x] as x goes to infinity is zero and the limit of its derivative does not exist.

    Thx
    Looks pretty straight forward: since cos(t) always lies between -1 and 1,
    [tex]-1/x\le cos(x^2)/x\le 1/x[/itex]. As x goes to infinity, both -1/x and 1/x go to 0.


    As for proving that "the limit of its derivative does not exist", what is the derivative of \(cos(x^2)/x\)?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: August 26th 2010, 10:59 AM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. Replies: 1
    Last Post: February 5th 2010, 03:33 AM
  4. Replies: 16
    Last Post: November 15th 2009, 04:18 PM
  5. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 05:05 PM

Search Tags


/mathhelpforum @mathhelpforum