It is wrong . Simply \(\displaystyle 0^\infty =0\).\(\displaystyle \lim_{x\rightarrow \infty} (\pi /2 - \arctan(x))^{x} =\lim_{x\rightarrow \infty} (1+[\pi /2 - \arctan(x)-1])^{\displaystyle x\cdot \displaystyle \frac{\pi/2 - \arctan(x)-1}{\pi/2 - \arctan(x)-1}}=\lim_{x\rightarrow \infty} e^{x(\pi /2 -\arctan(x)-1)}=\lim_{x\rightarrow \infty}e^{-x}=0\).