Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By Prove It
  • 1 Post By Prove It

Math Help - Find Discontinuity And Classifying Them

  1. #1
    Member
    Joined
    May 2011
    Posts
    178
    Thanks
    6

    Find Discontinuity And Classifying Them

    The problem I am looking at is f(x) = \frac{x - 3}{x^2 - 9}

    I found that f was not defined at x = \pm 3

    I have -3 as a non-removable discontinuity, and 3 as a removable discontinuity, approaching positive infinity from either side. Yet, when I graph the function, it is unequivocally approaching a finite value. Why did limiting process give me positive infinity?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,548
    Thanks
    1418

    Re: Find Discontinuity And Classifying Them

    Quote Originally Posted by Bashyboy View Post
    The problem I am looking at is f(x) = \frac{x - 3}{x^2 - 9}

    I found that f was not defined at x = \pm 3

    I have -3 as a non-removable discontinuity, and 3 as a removable discontinuity, approaching positive infinity from either side. Yet, when I graph the function, it is unequivocally approaching a finite value. Why did limiting process give me positive infinity?
    Notice that if \displaystyle \begin{align*} x \neq 3 \end{align*}, we have

    \displaystyle \begin{align*} \frac{x - 3}{x^2 - 9} &\equiv \frac{x - 3}{(x - 3)(x + 3)} \\ &\equiv \frac{1}{x + 3} \end{align*}

    The left hand limit as \displaystyle \begin{align*} x \to -3 \end{align*} is \displaystyle \begin{align*} -\infty \end{align*} while the right hand limit as \displaystyle \begin{align*} x \to -3 \end{align*} is \displaystyle \begin{align*} +\infty \end{align*}. Since the left and right hand limits are not equal, this is a jump discontinuity.
    Thanks from Bashyboy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2011
    Posts
    178
    Thanks
    6

    Re: Find Discontinuity And Classifying Them

    Oh, so you can cancel out factors; I thought I remembered my teacher saying we couldn't, or maybe that was just in the original function.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,548
    Thanks
    1418

    Re: Find Discontinuity And Classifying Them

    Quote Originally Posted by Bashyboy View Post
    Oh, so you can cancel out factors; I thought I remembered my teacher saying we couldn't, or maybe that was just in the original function.
    You can cancel out factors as long as you realise that there is an extra discontinuity in your original function.
    Thanks from Bashyboy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Classifying Groups
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 3rd 2011, 12:03 AM
  2. Help classifying a series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 14th 2010, 11:33 AM
  3. [SOLVED] Classifying functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: June 27th 2010, 01:59 PM
  4. Help classifying DEs.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: June 21st 2010, 05:42 PM
  5. Replies: 2
    Last Post: November 27th 2008, 04:44 PM

Search Tags


/mathhelpforum @mathhelpforum