Results 1 to 4 of 4

Math Help - computing limit

  1. #1
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52

    computing limit

    I am not sure how to go about computing this limit. I know the answer is -1/36.
    Though, I am having difficulties with the preliminary algebra and simplification so that I can make x = to 6.

     \lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,751
    Thanks
    484

    Re: computing limit

    Quote Originally Posted by raymac62 View Post
    I am not sure how to go about computing this limit. I know the answer is -1/36.
    Though, I am having difficulties with the preliminary algebra and simplification so that I can make x = to 6.

     \lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}
    start by getting a common denominator to combine the two fractions in the numerator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2011
    From
    Toronto
    Posts
    52

    Re: computing limit

    I just figured it out before I checked this! Can't believe what I was missing. Thanks though.

     \lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}

    = \lim_{x \to 6} \frac{\frac{x-6}{6x}}{6-x}

    = \lim_{x \to 6} \frac{x-6}{6x(6-x)}

    = \lim_{x \to 6} \frac{x-6}{36x - 6x^2}

    = \lim_{x \to 6} \frac{x-6}{-6x(-6+x)}

    = \lim_{x \to 6} \frac{1}{-6x}

    =  -\frac {1}{36}
    Last edited by raymac62; October 18th 2011 at 04:10 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,751
    Thanks
    484

    Re: computing limit

    Quote Originally Posted by raymac62 View Post
    I just figured it out before I checked this! Can't believe what I was missing. Thanks though.

     \lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}

    = \lim_{x \to 6} \frac{\frac{x-6}{6x}}{6-x}

    = \lim_{x \to 6} \frac{x-6}{6x(6-x)}

    = \lim_{x \to 6} \frac{x-6}{36x - 6x^2}

    = \lim_{x \to 6} \frac{x-6}{-6x(-6+x)}

    = \lim_{x \to 6} \frac{1}{-6x} = -\frac {1}{36}
    fixed the next-to-last line
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Computing A^k
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: September 19th 2011, 01:51 PM
  2. computing a limit
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 3rd 2011, 11:48 AM
  3. Computing ROI ?
    Posted in the Business Math Forum
    Replies: 1
    Last Post: May 13th 2009, 02:46 PM
  4. Computing e^A
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: November 27th 2008, 06:49 AM
  5. computing
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 28th 2007, 12:25 AM

/mathhelpforum @mathhelpforum