Results 1 to 2 of 2

Math Help - Prove norm of continuously differentiable function - repost from "urgent"

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    Prove norm of continuously differentiable function - repost from "urgent"

    Hello everyone, I might be breaking all rules by reposting my question here as well but the "urgent homework" forum did not quite seem to be the right place.

    Can someone prove that for any continuously differentable function on :


    Yes I know I am supposed to do it and I assume Cauchy-Schwarz is somehow involved but I cannot make out the details

    Best regards and thanks,
    Thomas
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Cauchy–Schwarz in \mathbb{R}^2 tells you that

    \begin{aligned}|f(t)\cos t-f'(t)\sin t| &= |(f(t),f'(t))\mathbf{\cdot}(\cos t,-\sin t)|\\ &\leqslant<br />
\left(|f(t)|^2+|f'(t)|^2\right)^{1/2}\left(\cos^2t+\sin^2t\right)^{1/2}. \end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 23rd 2011, 06:43 AM
  2. Replies: 2
    Last Post: April 24th 2011, 08:01 AM
  3. Norm vectorial space: an "enigma"
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 23rd 2011, 04:52 PM
  4. Replies: 1
    Last Post: October 25th 2010, 05:45 AM
  5. Differentiable, continuous function... "show that"
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 21st 2009, 04:01 AM

Search Tags


/mathhelpforum @mathhelpforum