I am trying to prove that the upper +limit of x^x, when x->0 converges to 1.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# X ln(x)

**Physics Forums | Science Articles, Homework Help, Discussion**