Results 1 to 4 of 4

Math Help - Analysis

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    20

    Analysis

    Hey all,

    I was wondering if there is a function such that
    a) f(3) exists, lim x->3 f(x) exists, but f is not continuous at 3

    Does such a function exist? or is it impossible?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by thahachaina View Post
    Hey all,

    I was wondering if there is a function such that
    a) f(3) exists, lim x->3 f(x) exists, but f is not continuous at 3

    Does such a function exist? or is it impossible?
    The following function satisfies your criteria:

    f(x) = | x- 3|, x \neq 0, and at x = 3 f(x) = 1.

    There are an infinite number of other functions that also satisfy the criteria.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    20
    Hey man, thanks for the help. But i didn't get how is f(x)=1 when x=3? Also, does x is not equal to zero a condition? Sorry if thats dumb, but could you please explain a little. Thanks once again
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by thahachaina View Post
    Hey man, thanks for the help. But i didn't get how is f(x)=1 when x=3? Also, does x is not equal to zero a condition? Sorry if thats dumb, but could you please explain a little. Thanks once again
    I have defined the following function:

    I have defined f(x) = |x - 3| for all values of x except for x = 3. When x = 3 I have defined the function to equal 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Analysis please :)
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 16th 2009, 04:38 AM
  2. analysis help
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 8th 2009, 03:11 PM
  3. analysis help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 19th 2009, 02:38 PM
  4. analysis
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 15th 2008, 03:07 PM
  5. Analysis Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 8th 2008, 05:59 PM

Search Tags


/mathhelpforum @mathhelpforum