Find the supremum and infimum limits for each sequence given below.

a. \(x_{n}=(-1)^{n}\left(1+n^{-1}ight)\)

b. \(x_{n}=(-1)^{n}\)

c. \(x_{n}=(-1)^{n} n\)

d. \(x_{n}=n^{2} \sin ^{2}\left(\frac{1}{2} n \piight)\)

e. \(x_{n}=\sin (n)\)

f. \(x_{n}=\left(1+n^{-1}ight) \cos (n \pi)\)

g. \(x_{n}=\sin \left(\frac{1}{2} n \piight) \cos \left(\frac{1}{2} n \piight)\)

h. \(x_{n}=(-1)^{n} n(1+n)^{-n}\)