Why does [math]\displaystyle \lim_{x\to \infty } \, \left(\frac{\left(1+\frac{1}{x}\right)^x}{e}\right)^x = \frac{1}{\sqrt{e}}?[/math]
[math]\displaystyle \lim_{x \to 0} \left(\frac{1}{x^2}-\frac{1}{\tan^2 x}\right) =[/math] ?