Results 1 to 4 of 4

Math Help - Show that x*sin(1/x) is continuous. Help~

  1. #1
    Junior Member
    Joined
    Nov 2012
    From
    Taiwan
    Posts
    41

    Show that x*sin(1/x) is continuous. Help~

    Well, the problem is...
    how do I show that f(x)= x*sin(1/x) for 0<x<=1 and f(0)=0 is continuous on [0,1]?
    Can anyone help me with this problem?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: Show that x*sin(1/x) is continuous. Help~

    Quote Originally Posted by Rita View Post
    Well, the problem is...
    how do I show that f(x)= x*sin(1/x) for 0<x<=1 and f(0)=0 is continuous on [0,1]?
    All you need is to show that {\lim _{x \to {0^ + }}}x\sin \left( {\frac{1}{x}} \right) = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2012
    From
    Taiwan
    Posts
    41

    Re: Show that x*sin(1/x) is continuous. Help~

    I'm sorry, but why is that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: Show that x*sin(1/x) is continuous. Help~

    Quote Originally Posted by Rita View Post
    I'm sorry, but why is that?
    Do you have any idea what it means for f to be continuous of [0,1]~?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show that sin(x) is continuous
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 24th 2012, 11:57 AM
  2. Show that h is continuous on D.
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: March 22nd 2010, 06:38 PM
  3. show that f is continuous at -3
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 21st 2010, 05:58 PM
  4. Show that f(x) = 1/x is continuous at x=5.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 8th 2010, 12:00 PM
  5. show 1/x is continuous at x = c > 0
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 30th 2008, 05:40 PM

Search Tags


/mathhelpforum @mathhelpforum