Repeat Problem 4.2-3 with \(T=0.01 \mathrm{~s}\).

Problem 4.2-3. 

Find the \(z\)-transform of the following functions, using \(z\)-transform tables. Compare the pole-zero locations of \(E(z)\) in the \(z\)-plane with those of \(E(s)\) and \(E^{*}(s)\) in the \(s\)-plane (see Problems 3.4-1). Let \(T=0.5 \mathrm{~s}\).

(a) \(E(s)=\frac{10}{(s+1)(s+3)}\)

(b) \(E(s)=\frac{s+7}{s(s+3)}\)

(c) \(E(s)=\frac{s+2}{s(s+1)}\)

(d) \(E(s)=\frac{s+2}{s^{2}(s+1)}\)

(e) \(E(s)=\frac{s^{2}+3 s+2}{s(s+1)(s+2)}\)

(f) \(E(s)=\frac{2}{s^{2}+2 s+5}\)