Results 1 to 3 of 3

Math Help - limited thoughts on limits :S

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    14

    limited thoughts on limits :S

    Please help me solve this question:

    lim (x^3-3x-2)/
    x->2 (x^2-5x+6)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by redpanda11 View Post
    Please help me solve this question:

    lim (x^3-3x-2)/
    x->2 (x^2-5x+6)
    factorize the numerator and denominator and your problem will cancel out. (note that (x - 2) is a factor of the cubic in the numerator)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by redpanda11 View Post
    Please help me solve this question:

    lim (x^3-3x-2)/
    x->2 (x^2-5x+6)
    \lim_{x \to 2} \frac{x^3 - 3x - 2}{x^2 - 5x + 6}

    Note that x - 2 is a factor of x^3 - 3x - 2, evidenced by the fact that 2^3 - 3 \cdot 2 - 2 = 0.

    Thus, by long or synthetic division we get that
    x^3 - 3x - 2 = (x - 2)(x + 1)^2

    The denominator factors.

    Thus
    \lim_{x \to 2} \frac{x^3 - 3x - 2}{x^2 - 5x + 6} = \lim_{x \to 2} \frac{(x - 2)(x + 1)^2}{(x - 2)(x - 3)}

    = \lim_{x \to 2} \frac{(x + 1)^2}{x - 3}

    = \frac{9}{-1} = -9

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Thoughts on the empty set and logic
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: April 3rd 2011, 08:21 PM
  2. Any thoughts on this Proof?
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 14th 2011, 03:38 PM
  3. Working with sec...any thoughts
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 29th 2010, 04:19 PM

Search Tags


/mathhelpforum @mathhelpforum