Limit x→0+ x^(1/x - 1): Is It Defined?

[daniel_i_l]

Homework Statement

I was doing a problem and got to the following limit:
lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1} I calculated it and got 0 but when I calculated it here:
http://wims.unice.fr/wims/en_tool~analysis~function.en.html
It said that it wans't defined. Am I right?
Thanks.

Homework Equations

The Attempt at a Solution

 

[sutupidmath]

try the following:
lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1}=\lim_{x\rightarrow 0^{+}}e^{ln(x)^{\frac{1}{x}-1}}=\lim_{x\rightarrow\ 0^{+}} e^{\frac{1-x}{x}ln(x)}=e^{\lim_{x\rightarrow\ 0^{+}}\frac{1-x}{x} \lim_{x\rightarrow\ 0^{+}}ln(x)}=e^{\infty*(-\infty)}=e^{-\infty}=0

 

[daniel_i_l]

Thanks, that's what I did but the wims calculator confused me.