(a) (i) Sketch the Bode magnitude plot for the function

\[T(s)=\frac{10(s+10)(s+100)}{(s+1)(s+1000)}\]

(ii) What are the corner frequencies?

(iii) Determine \(|T(\omega)|\) for \(\omega \rightarrow 0\).
(iv) Determine \(|T(\omega)|\) for \(\omega \rightarrow \infty\).

(b) Repeat part (a) for the function \[T(s)=\frac{8 s^{2}}{(0.2 s+1)^{2}}\]