Results 1 to 3 of 3

Math Help - Limit problem

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    41

    Limit problem

    First, congrats to forum admins and all contributors for this miracoulous forum.

    I'm having some trouble solving limx->-3 (x^3+5x^2+3x-9)/(x^3-3x^2-45x-81)

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,904
    Thanks
    765
    Hello, GreenMile!

    \lim_{x\to\,\text{-}3}\:\frac{x^3+5x^2+3x-9}{x^3-3x^2-45x-81}

    If x = -3, the fraction becomes \frac{0}{0}

    Hence, (x+3) is a factor of both polynomials.


    The numerator factors: . x^3+5x^2 + 3x - 9 \:=\:(x+3)(x^2+2x-3) \;=\;(x+3)(x-1)(x+3)

    The denominator factors: . x^3-3x^2-45x-81 \;=\;(x+3)(x^2-6x-27) \;=\;(x+3)(x+3)(x-9)


    The problem becomes: . \lim_{x\to\:\text{-}3}\frac{({\color{blue}\rlap{/////}}x+3)(x-1)({\color{red}\rlap{/////}}x+3)}{({\color{blue}\rlap{/////}}x+3)({\color{red}\rlap{/////}}x+3)(x-9)} \;=\;\lim_{x\to\:\text{-}3}\frac{x-1}{x-9} \;=\;\frac{-4}{-12} \;=\;\frac{1}{3}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    41
    Thank you very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: August 13th 2010, 02:03 AM
  2. Replies: 1
    Last Post: August 8th 2010, 12:29 PM
  3. Another Limit Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 30th 2010, 02:19 AM
  4. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 06:05 PM
  5. Limit Problem
    Posted in the Calculus Forum
    Replies: 10
    Last Post: March 20th 2007, 12:54 PM

Search Tags


/mathhelpforum @mathhelpforum