Integrujte $f(z)=e^{iz}/z$ p�es $\varphi _{r,R}$
kde $\varphi _{r,R}$ je kladn� orientovan� obvod mno�iny
$$
\{z \in \Bbb C : r < |z| < R, \Cal A rg (z) \in [0, \pi] \} \quad .
$$
Zkoumejte limitu pro $R \to \infty$ a $r \to 0$
$$
\lim _{R \to \infty, r \to 0} \int _{\varphi _{R,r}} f(z) dz  \quad .
$$
Plat�
$$
\int _0 ^{\infty} \dfrac{\sin (t)}{t} dt = \dfrac{\pi}{2} \quad .
$$
