Help with limits and L'Hopital's Rule

[MAM]

I need help solving the following:

lim x^x
x ->0+

lim (1 - (1/n))^n
n -> infinity

Any help would be much appreciated!!

 

[daon2]

Find these limit first:

\(\displaystyle \displaystyle \lim_{x\to 0^+}\,\ln x^x = \lim_{x\to 0^+}\,x\ln x \)


\(\displaystyle \displaystyle \lim_{n\to\infty}\,\ln\left(1-\frac{1}{n}\right )^n =\lim_{n\to\infty}\,n\ln\left(1-\frac{1}{n}\right )\)