Limits and indeterminate Powers

Find the limit  $\lim_{x\rightarrow1^+}\ \ \left(x\right)^{\frac{1}{\left(1-x\right)}}$  

 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow\infty}\ \ \ \left(\ln\ x\right)^{\frac{1}{x}}$  

 $f\left(x\right)=x^{\frac{1}{\left(x-1\right)}}$ leads to a form 

 $Find\$  

 $\lim_{x\rightarrow0^+}\ \ \ \left(1+\frac{1}{x}\right)^x$  

 $\lim_{x\rightarrow\infty}\left(1+2x\right)^{\frac{1}{2\ln x}}$  

 $\infty$   $\lim_{x\rightarrow\infty}x^2\ e^{-x}$  

 $\lim_{x\rightarrow0}\ \frac{e^{x\ }-\left(1+x\right)}{x^2}$