Results 1 to 3 of 3

Math Help - Help understanding the delta-epsilon definition of a limit!!

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    40

    Help understanding the delta-epsilon definition of a limit!!

    Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number.
    means that
    for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |xc| < δ, we have |f(x) − L| < ε. or, symbolically,
    My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.




    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2008
    Posts
    36
    Quote Originally Posted by jpatrie View Post
    My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.

    Epsilons and deltas can be pretty overwhelming when you first experience them. Epsilon (e) and delta (d) are just error bounds. You can think of them as small positive real numbers.

    In words, lim (x->c) f(x) = L means for any number x in your interval, the closer x is to c, the closer f(x) will be to L.

    Note |x-c| just denotes the distance between x and c, or the absolute value of the difference.

    So saying "for any e>0 there exists d>0, any for any x, 0<|x-c|<d -> |f(x)-L|<e" means

    For ANY small distance e, if the distance between f(x) and L is less than e, than you can ALWAYS find a d so that the distance between x and c is less than d.

    Hope this helps! It easier to explain with pictures.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jpatrie View Post
    My main confusions are with the symbols used, and what they mean, my textbook for my math course was designed by fresh grad students, and it doesn't really identify what all that stuff mean.




    Try reading this: http://www.mathhelpforum.com/math-he...ta-proofs.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Epsilon delta definition of limit.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 20th 2011, 07:20 PM
  2. Replies: 3
    Last Post: February 21st 2011, 09:11 AM
  3. Epsilon delta definition of limit
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 7th 2010, 12:39 AM
  4. How is my understanding of N-epsilon definition of a limit?
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 4th 2010, 06:59 AM
  5. Epsilon-Delta Limit Definition
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2009, 03:20 PM

Search Tags


/mathhelpforum @mathhelpforum