Given $f(z)= e^{\frac {\sin z}{z}} $, show that it has a removable singularity at $z=0$ and essential singularity at $z=k\pi$ for $k \geq 2$
It is easy to check that limit exists at $z =0$ for $\frac {\sin z}{z} (=1)$, so it has removable singularity, but limit also exists at $z=k\pi$ $(\lim =0)$ , then how does it have an essential singularity there?