Results 1 to 4 of 4

Math Help - Problem using l'hopital rule

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    3

    Problem using l'hopital rule

    Hi all

    I have encountered a problem when applying the l'hopital rule to the following limit; could anyone help to see where i went wrong?

    lim x->infinity (1+e^x+2e^2x) / (x+e^x+e^2x) ------(1);

    repeating application of the rule gives:


    lim x->infinity (e^x+4e^2x) / (1+e^x+4e^2x);

    which then gives

    lim x->infinity (e^x+8e^2x) / (e^x+8e^2x) = 1;


    However in the solution provided, e^-2x is multiplied to (1), giving:


    lim x->infinity (e^-2x+e^-x+2) / (xe^-2x+e^-x+1) = 2/1 = 2;


    which is different from my answer.

    Any help is much appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member integral's Avatar
    Joined
    Dec 2009
    From
    Arkansas
    Posts
    200
    EDIT: l'hoptials rule does not apply to this function. here is how you solve it:
    \displaystyle\lim_{x\rightarrow \infty}\frac{1+e^x+2e^{2x}}{x+e^x+e^{2x}}

    \displaystyle\lim_{x\rightarrow \infty}\frac{\frac{1}{e^{2x}}+\frac{1}{e^x}+2}{\fr  ac{x}{e^{2x}}+\frac{1}{e^x}+1}


    =\frac{2}{1}
    Last edited by integral; February 27th 2011 at 08:54 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    In your solution, even after second derivative, the problem is in indeterminate form. Because it is a fraction of infinity/infinity. So you have to remove e^x from the numerator and denominator. That is what you have seen in the solution.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2011
    Posts
    3
    Thanks for the replies; upon double checking i realised that i have differentiated one part wrongly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit Problem (L'Hopital's Rule)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 4th 2010, 02:56 PM
  2. Limit problem (maybe L'Hopital's Rule)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2010, 10:51 AM
  3. problem's w/ l'hopital's rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 28th 2009, 08:25 PM
  4. L'Hopital's Rule (a different problem)
    Posted in the Calculus Forum
    Replies: 8
    Last Post: July 28th 2009, 07:37 PM
  5. Replies: 2
    Last Post: October 24th 2008, 04:00 PM

Search Tags


/mathhelpforum @mathhelpforum