Evaluate the limit $\displaystyle\lim_{x \to 0^{+}} x \cdot \ln(x)$ I have this assignment 
Evaluate the limit:
5.$\displaystyle\lim_{x \to 0^{+}} x \cdot \ln(x)$
I don't think we are allowed to use L'Hopital, but I can't imagine how else. 

If you set $y=\ln x$, you can rewrite it as $\lim_{x\to-\infty}ye^y=-\lim_{y\to\infty}\frac{y}{e^y}$, and you probably know what that is. Of course that approach requires that you be allowed to use known limits.
