Results 1 to 3 of 3

Thread: Continuity

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    California
    Posts
    28
    Thanks
    4

    Continuity

    Let f(x) be a continuous function in R. If the limit $\displaystyle \lim_{x\to\2} \frac{|f(x-2)| + |x-2|}{x-2}$ exists and it is a real number, find the value of $\displaystyle \alpha$ so that the function g(x) = $\displaystyle \lim_{x\to\2} \frac{|f(x-2)| + |x-2|}{x-2} \quad for \quad x \ne 2$
    $\displaystyle \alpha \quad for \quad x = 2 $

    is continuous

    I am trying to prove that g(x) is differentiable, because when a function is differentiable is continuous as well, but I can't. Can anyone help?
    Last edited by ManosG; Mar 30th 2013 at 08:21 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,742
    Thanks
    2814
    Awards
    1

    Re: Continuity

    Quote Originally Posted by ManosG View Post
    Let f(x) be a continuous function in R. If the limit $\displaystyle \lim_{x\to\2} \frac{|f(x-2)| + |x-2|}{x-2}$ exists and it is a real number, find the value of $\displaystyle \alpha$ so that the function g(x) = $\displaystyle \lim_{x\to\2} \frac{|f(x-2)| + |x-2|}{x-2} \quad for \quad x \ne 0$
    $\displaystyle \alpha \quad for \quad x = 2 $ is continuous

    I think that you mean $\displaystyle g(x) = \left\{ {\begin{array}{rl} {\dfrac{{|f(x - 2)| + |x - 2|}}{{x - 2}},}&{x \ne 2} \\ {\alpha ,}&{x = 2} \end{array}} \right.$

    If that is correct then $\displaystyle \lim_{x\to\2} \frac{|f(x-2)| + |x-2|}{x-2}=L=\alpha.$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    California
    Posts
    28
    Thanks
    4

    Re: Continuity

    Only that? We can't find a specific value?? Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Feb 16th 2013, 06:38 AM
  2. Continuity
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Feb 3rd 2011, 02:22 PM
  3. WOT continuity
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 17th 2010, 11:42 PM
  4. Continuity, Uniform Continuity
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Feb 1st 2009, 08:36 PM
  5. Continuity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 22nd 2008, 02:40 PM

Search Tags


/mathhelpforum @mathhelpforum