# Homework Help: A limit question

1. Mar 18, 2008

### daniel_i_l

1. The problem statement, all variables and given/known data
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:
It said that it wans't defined. Am I right?
Thanks.

2. Relevant equations

3. The attempt at a solution

2. Mar 18, 2008

### sutupidmath

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

3. Mar 18, 2008

### daniel_i_l

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