Show that all the singular points of the following functions

Show that all the singular points of the following functions are poles. Determine the order of each pole and the corresponding residue.

z + 1/z2 ? 2z

tanh z

z/cos z

Find the residue at z = 0 for the following functions:
csc² z z^-3

csc(z²2)

zcos(1/z)

Solution

the pole i found was z = ?/2 + 2n? and -?/2 +2n? i attempted to find the residues using limits. limz??/2 + 2n? (z-(?/2 + 2n?)) z/cosz doing some annoying algebra and just evaluating at ?/2 + 2n? i get 0/0. so i can use L\'hopitals rule, right? doing so i get my limit to equal ?/2 + 6n?