40) Find the first 5 terms of the Taylor series of around .

41) Find the Taylor series of around . (Suggestion: Use the identity .)

42) Find the first four nonzero terms in the Taylor series of

around .

43) Find the Taylor expansion of

around . (Suggestion: First do a partial fraction decomposition.)

44) Find the Taylor expansion of

around .

45) Find the first 5 nonzero terms in the Laurent expansion of around .

46) Find the terms of nonpositive index in the Laurent expansion of

around .

47) Find the points where

is singular (i.e. not analytic). Find its residues at those points.

48) Same as the previous question, but with

.

49) Same as the previous question, but with

.