\lim_{x \to 0}{(\frac{arctgx}{x})^{\frac{1}{x^2}}}=\lim_{x \to 0}{(1 + \frac{arctgx}{x} -1 )^{\frac{1}{x^2}}}= \lim_{x \to 0}{(1 + \frac{arctgx -x}{x})^{\frac{1}{x^2}}}=