Results 1 to 2 of 2

Thread: real analysis

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    real analysis

    1a) suppose that f is continuous on [a b] and differentiable on (a b) with f(a) = f(b) = 0. Show that for every k in R, there exists a c in (a b) with f '(c) = kf(c). (Hintconsider the function g(x) = exp^(-kx)f(x) for x in [a b]

    b) sho that f(x) = sinx is unformly continuos on R. (Hint: if |x-y|< delta, use the Mean Value Theorem on [x y].)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,656
    Thanks
    14
    your problems are already solved, wonder why you didn't attach any attempt of solution.

    given $\displaystyle g(x)=e^{-kx}f(x),$ since $\displaystyle g(a)=g(b)=0$ then exists $\displaystyle c\in(a,b)$ so that $\displaystyle g'(c)=-ke^{-kc}f(c)+e^{-kc}f'(c)=0\implies f'(c)=kf(c).$

    the second one has been proved many times here, i suggest to you to use the seach engine.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Two Real Analysis Q's
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Jan 29th 2011, 01:15 PM
  2. real analysis
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Sep 12th 2009, 08:29 AM
  3. real analysis
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: Sep 7th 2009, 05:16 PM
  4. Real Analysis Help!!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Dec 6th 2008, 06:38 PM
  5. Real Analysis
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 19th 2006, 10:37 AM

Search Tags


/mathhelpforum @mathhelpforum