lim_x->Unendlich x(arctan(x)-pi/2)
lim (x → ∞) x·(ARCTAN(x) - pi/2)
= lim (x → ∞) (ARCTAN(x) - pi/2) / (1/x)
L'Hospital
= lim (x → ∞) 1/(x^2 + 1) / (- 1/x^2)
= lim (x → ∞) - x^2/(x^2 + 1)
= lim (x → ∞) - 1/(1 + 1/x^2) = - 1/(1 + 0) = - 1
