Find the Taylor series centered at \(x=a\) and its corresponding radius of convergence for the given function. In most cases, you need not employ the direct method of computation of the Taylor coefficients.

a. \(f(x)=\sinh x, a=0\).

b. \(f(x)=\sqrt{1+x}, a=0\).

c. \(f(x)=\ln \frac{1+x}{1-x}, a=0\).

d. \(f(x)=x e^{x}, a=1\).

e. \(f(x)=\frac{1}{\sqrt{x}}, a=1\)

f. \(f(x)=x^{4}+x-2, a=2\).
g. \(f(x)=\frac{x-1}{2+x}, a=1\).