Results 1 to 10 of 10
Like Tree4Thanks
  • 2 Post By Plato
  • 1 Post By Plato
  • 1 Post By johng

Math Help - Limit question,

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Exclamation Limit question,

    Hey guys not sure where to go with this, I am generally ok with delta epsilon questions but Im stuck here. I have a Summer test Thursday and supposedly something similar will come up.

    Suppose that f
    (x) approaches L as x approaches a.
    Show that there corresponds to each positive number E (epsilson) a positive number d (delta) such that,
    |f(x1)-f(x2)| < E

    for every choice of x1and x2 in
    I( a, d ).
    Last edited by MathJack; May 7th 2013 at 02:48 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1

    Re: Limit question,

    Quote Originally Posted by MathJack View Post
    Hey guys not sure where to go with this, I am generally ok with delta epsilon questions but Im stuck here. I have a Summer test Thursday and supposedly something similar will come up.
    Suppose that f(x) approaches L as x approaches a. Show that there corresponds to each positive number E (epsilson) a positive number d (delta) such that,
    |f(x1)-f(x2)| < E
    for every choice of x1and x2 in I( a, d ).
    There is a real puzzle contained in your question.
    That question asks you to prove a what the vast majority of Authors and Textbooks use as the definition of limit.

    So your text material must use a different definition. What definition of limit do you have?
    Thanks from topsquark and MathJack
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Re: Limit question,

    Sorry its on a pdf,

    'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)

    If f has a limit L at a we write

    lim f(x) = L or f(x) approaches L as x approaches a
    '

    And thats it
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Re: Limit question,

    A better layout of the definition and question are on the sheet. Sorry about the delay, wasnt sure if it would come up
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1

    Re: Limit question,

    Quote Originally Posted by MathJack View Post
    Sorry its on a pdf,
    'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)
    If f has a limit L at a we write
    lim f(x) = L or f(x) approaches L as x approaches a

    Sorry, I will not open an attached file.
    If you are to lazy to type it out using LaTeX, then you may be out of luck.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Re: Limit question,

    I do not know how to use LaTex yet

    'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)

    If f has a limit L at a we write

    lim f(x) = L or f(x) approaches L as x approaches a
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1

    Re: Limit question,

    Quote Originally Posted by MathJack View Post
    'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)
    If f has a limit L at a we write lim f(x) = L or f(x) approaches L as x approaches a
    That is in a deleted neighborhood of a.
    That simply means that if 0<|x-a|<\delta then |f(x)-L|<\epsilon .

    What happen if we drop the deleted neighborhood part?

    Suppose it is true on the non-deleted neighborhood, is it true on the deleted neighborhood ?
    Thanks from MathJack
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    639
    Thanks
    257

    Re: Limit question,

    Hi,
    Here's a proof of what you want. The triangle inequality is used; you'll definitely see this usage again as you progress. However, in asking questions, you should be very careful to ask the exact question. Your original post left out the deleted neighborhood which makes the statement false.

    Limit question,-mhfcalc6.png
    Last edited by johng; May 7th 2013 at 04:54 PM.
    Thanks from MathJack
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Re: Limit question,

    If we drop the deleted neighborhood part then |f(x)-L| < E is always true, no restrictions?

    So if it is true on the non-deleted neighborhood then for the same values it must be true on the deleted neighborhood. (this can be said for an infinite number of larger NDNs). And if true on the DN then |f(x1) - f(x2)| < E must be true?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Feb 2013
    From
    cork
    Posts
    68
    Thanks
    7

    Re: Limit question,

    Quote Originally Posted by johng View Post
    Hi,
    Here's a proof of what you want. The triangle inequality is used; you'll definitely see this usage again as you progress. However, in asking questions, you should be very careful to ask the exact question. Your original post left out the deleted neighborhood which makes the statement false.

    Click image for larger version. 

Name:	MHFcalc6.png 
Views:	7 
Size:	9.9 KB 
ID:	28286
    Cheers johng, triangle inequality..bingo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 7th 2011, 03:27 PM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. another limit question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 20th 2009, 05:15 AM
  4. limit question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 14th 2009, 08:35 PM
  5. a limit question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 13th 2009, 12:44 PM

Search Tags


/mathhelpforum @mathhelpforum