Results 1 to 3 of 3

Thread: Confused about undefined values

  1. #1
    Sep 2012

    Confused about undefined values

    If I have an equation such as y = (3x(1-x))/(1-x) this simplifies to y = 3x?

    but if x = 1 the first equation is undefined though for the second y = 3

    could somebody please explain what is going on here?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas

    Re: Confused about undefined values

    the function has a point discontinuity (a "hole") at the coordinates (1,3)
    Attached Thumbnails Attached Thumbnails Confused about undefined values-hole.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Mar 2011

    Re: Confused about undefined values

    the simplest example is:

    y = x/x

    for every x EXCEPT 0, we have y = 1. at x = 0, y is undefined.

    it seems like we ought to just be able to "get around this" by simply using THIS function instead:

    y = x/x, for x ≠ 0
    y = 1, if x = 0

    which is what we really want.

    a while ago (around 450 years, give or take) some clever guys discovered a way to deal with this "pesky vanishing 0 in the denominator"...use LIMITS!

    the idea is to use what x/x is "heading to" at x = 0, without letting x actually "touch 0". since this is clearly 1 (in this example), we can "plug the hole" obtaining the "defined everywhere" function we really want, and not some bad one with a point of "un-definition".

    unfortunately, limits turn out to be, in general, kind of complicated (this particular one isn't so bad). there's these things called epsilons and deltas which can make your head hurt (mathematicians love fancy names for "itty-bitty numbers").

    what you have discovered (albeit unwittingly) is that:

    $\displaystyle \lim_{x \to 1} \frac{3x(1-x)}{1-x} = 3$

    even though 0/0 makes no sense at all.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] For what values of x will F be undefined?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Apr 9th 2010, 03:44 PM
  2. Replies: 2
    Last Post: Jan 10th 2010, 08:45 AM
  3. undefined
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: Jul 30th 2008, 04:54 AM
  4. finding undefined values
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Aug 31st 2007, 01:27 PM
  5. undefined
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Jan 27th 2007, 02:10 PM

Search Tags

/mathhelpforum @mathhelpforum