Results 1 to 2 of 2

Math Help - L'Hopital's Rule question...

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    17

    L'Hopital's Rule question...

    Hi, I have two questions requiring L'Hopital's Rule that I can't seem to get. They are


    And



    For the first one I didn't even think the rule was necessary. I thought I could just plug in infinity and get (1+0)^INF. But this was obviously wrong. For the second I thought I should try to get it into a quotient problem, but I kept getting 0 in the denominator. I'd really appreciate help. Thanks!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    let  y = \ln \Big(1 + \frac{9}{x}\Big) ^{\frac{x}{2}} =  \frac{x}{2} \ln \Big(1 + \frac{9}{x}\Big)  = \frac{\ln \Big(1 + \frac{9}{x}\Big)}{\frac{2}{x}}

    which is the indeterminate form  \frac{0}{0}

    so  \lim_{x \to \infty} y = \lim_{x \to \infty}  \frac{\ln \Big(1 + \frac{9}{x}\Big)}{\frac{2}{x}}

     = \lim_{x \to \infty}  \frac{\frac{1}{1+\frac{1}{9x}}* -\frac{9}{x^{2}}}{-\frac{2}{x^{2}}} = \frac{9}{2} \lim_{x \to \infty} \frac{1}{1+\frac{1}{9x}} = \frac{9}{2}*1 = \frac{9}{2}


    the original function is  e^{y}

    so  \lim_{x \to \infty} \Big(1 + \frac{9}{x}\Big) ^{\frac{x}{2}} = \lim_{x \to \infty} e^{y}  = e^{\frac{9}{2}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Very Simple Question on l'Hopital's Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 27th 2010, 06:47 PM
  2. Replies: 5
    Last Post: December 19th 2009, 10:14 PM
  3. L'Hopital's Rule question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 2nd 2009, 11:25 PM
  4. Need help with l'hopital rule question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 18th 2008, 07:29 PM
  5. L'Hopital's rule question
    Posted in the Calculus Forum
    Replies: 29
    Last Post: July 8th 2007, 09:10 AM

Search Tags


/mathhelpforum @mathhelpforum