Results 1 to 2 of 2

Math Help - ln Limit Problem

  1. #1
    Senior Member
    Joined
    Oct 2012
    From
    USA
    Posts
    404
    Thanks
    1

    ln Limit Problem

    Finally, this looks right:

    \lim x \rightarrow 1

    \dfrac{5x}{x - 1} - \dfrac{5}{\ln x}

    \dfrac{5(1)}{(1) - 1} - \dfrac{5}{\ln (1)}

    \dfrac{5}{0} - \dfrac{5}{0} = \dfrac{0}{0} Indeterminate

    \dfrac{5x}{x - 1} - \dfrac{5}{\ln x}

    \dfrac{5 \ln x}{(x - 1)(\ln x)} - \dfrac{5(x  - 1)}{(x - 1)(\ln x)}

    \dfrac{5 \ln x}{(x - 1)(\ln x)} - \dfrac{5x - 5}{(x - 1)(\ln x)}

    \dfrac{5 \ln x - 5x - 5}{\ln x^{2} - \ln x}

    \dfrac{5 \ln x - 5x - 5}{2 \ln x - \ln x}

    \dfrac{\dfrac{d}{dx} 5 \ln x - 5x - 5}{\dfrac{d}{dx} 2 \ln x - \ln x}

    \dfrac{\dfrac{5}{x} - 5}{\dfrac{2}{x} - \dfrac{1}{x}}

    \dfrac{\dfrac{5}{x} - 5}{\dfrac{1}{x}}

    \dfrac{\dfrac{5}{(1)} - 5}{\dfrac{1}{(1)}} = \dfrac{0}{1} = 0 Answer?? Computer still says no.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,655
    Thanks
    603

    Re: ln Limit Problem

    Hey Jason76.

    Hint: You should have [5x*ln(x) - 5(x-1)]/[(x-1)ln(x)] when you simplify both fractions into one compound one. See if this changes your answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: August 13th 2010, 01:03 AM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. limit Problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 17th 2009, 09:21 PM
  4. limit Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 15th 2009, 03:08 AM
  5. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 05:05 PM

Search Tags


/mathhelpforum @mathhelpforum