1. Limited time only! Sign up for a free 30min personal 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!

X ln(x)

  1. Oct 10, 2008 #1
    I am trying to prove that the upper +limit of x^x, when x->0 converges to 1.

    So I started by converting x^x to e^(x ln(x)). I know that this eliminates the domain: x <= 0, but I still believe that I can still continue on.

    So here I tried to constrain the limit: x ln(x) (i.e. x->0, x ln(x) -> 0; which is where I failed. Although I can show via the L'hopital's Rule that it is true, I struggle to show it via the Epsilon Delta Definition.

    I know that x^x is undefined at 0, but I still want to show that the curve converges towards 1.
  2. jcsd
  3. Oct 10, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Why not show that L'Hopitul's rule can be proven in general with the epsilon/delta-definition?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook