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Math Help - Definition of limit as x approaches infinity

  1. #1
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    Definition of limit as x approaches infinity

    Hi everyone!

    I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

    " We say that f(x) has the limit L as x approaches infinity and write

    lim x->∞ f(x) = L

    if for every number Є > 0 there exists a corresponding number M such that for all x

    x > M -> |f(x) - L| < Є "

    That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

    Thanks!
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    Re: Definition of limit as x approaches infinity

    Quote Originally Posted by Nora314 View Post
    Hi everyone!

    I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

    " We say that f(x) has the limit L as x approaches infinity and write

    lim x->∞ f(x) = L

    if for every number Є > 0 there exists a corresponding number M such that for all x

    x > M -> |f(x) - L| < Є "

    That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

    Thanks!
    M is an arbitarily large number that depends on epsilon.

    Just like delta was an arbitarily small number that depends of epsilon.

    So they are basically saying if we pick M big enough that for any x bigger than M f(x) is getting close to the limit (read less then epsilon)
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