Problem 1688 (difficulty: 4/10)

Find the singularities and residues of the following functions:

\(\displaystyle \frac1z; \quad \frac1{z^2}; \quad \frac1{z^2+2z}; \quad \quad \frac1{\sin z}; \quad \sin\frac1z; \quad \frac{e^z}{z^2+4}; \quad \frac{e^z}{(z^2+4)^2}; \quad \frac{e^z}{(z^2+4)^3} \quad \frac{e^z-z^3+8}{z^2+1} \)

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