Question

Sa se calculeze: subpunctul f).

Answer 1

 

$\displaystyle\\ \cos\dfrac{\pi}{2} =0\\\lim_{x \to \dfrac{\pi}{2} } \Big(\text{arctg}(x)\Big)^{\cos x}=\left(\text{arctg}\Big(\dfrac{\pi}{2}\Big)\right)^{\cos \dfrac{\pi}{2}}=\left(\text{arctg}\Big(\dfrac{\pi}{2}\Big)\right)^{0}=\boxed{1}$