(a) Determine the Taylor series representation centered at

z_(0)=0

for

f(z)=sinh(z)

and

g(z)=cosh(z)

, and find where they are\ valid.\ (b) Find the Taylor series representation centered at

z_(0)=1

of the function

f(z)=(1-z)/(z-3)

. Hint: use the identity\

f(z)=((z-1)/(2))(1)/(1-(z-1)/(2))

and use the geometric series representation.

(a) Determine the Taylor series representation centered at z0=0 for f(z)=sinh(z) and g(z)=cosh(z), and find where they are valid. (b) Find the Taylor series representation centered at z0=1 of the function f(z)=(1z)/(z3). Hint: use the identity f(z)=(2z1)1(z1)/21 and use the geometric series representation