Chapter 14.4, Problem 11P

For each of the following functions, say whether the indicated point is regular, an essential singularity, or a pole, and if a pole of what order it is.

(a) $\frac{e^z-1-z}{z^2},z=0$

(b) $\frac{\sin z}{z^3},z=0$

(c) $\frac{z^2-1}{{(z-1)}^2},z=1$

(d) $\frac{\cos z}{{(z-\pi /2)}^4},z=\pi /2$