1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limits question L'Hopitals rule

  1. Nov 15, 2007 #1
    1. The problem statement, all variables and given/known data
    lim (sin(x)/x)^(1/X^2)

    2. Relevant equations
    for the life of me i cannot get the correct solution

    3. The attempt at a solution
    Ive tried taking the log of both sides etc and working from there then applying l'hopitals rule until i get a result but the answer i always get is e^(-1/2) but the answer is e^(-1/6) any help would be much appreciated
  2. jcsd
  3. Nov 15, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    e^(-1/6) is correct. And that's the way to do it alright. But there is no way to tell why you get e^(-1/2) unless you show us what you did.
  4. Nov 15, 2007 #3
    sorry ill give more info
    lim (sin(x)/x)^(1/X^2)

    let y = (sin(x)/x)^(1/X^2)
    ln y = (ln(sin(x)/x))^(1/X^2)
    ln y = (ln(sin(x)/x))/(X^2)
    ln y = (ln sin(x) - ln(x))/(X^2)
    apply l'hopital's rule
    = (cos(x)/sin(x) - 1/y)/2X
    apply l'hotital's rule again
    = (-sin(x)/cos(x) -1/1)/2
    and from there i get
    = -1/2
    y = e^(-1/2)
    Last edited: Nov 15, 2007
  5. Nov 15, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    How did y get over on the right side?
    Applying L'Hopital's rule gives you
    [tex]\frac{\frac{cos(x)}{sin(x)}- 1/x}}{2x}[/tex]
    so I assume the "1/y" was "1/x". That reduces to
    [tex]\frac{xcos(x)- sin(x)}{2x^2sin(x)[/tex]
    You are also differentiating incorrectly. The derivative of cos(x)/sin(x) is NOT (cos(x))'/(sin(x))' and the derivative of 1/x is NOT1/(x)'!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Limits question L'Hopitals rule