Apply the initial and Final Value Theorems to find y ( 0 + ) y ( 0 + ) and y ( ) y

Apply the initial and Final Value Theorems to find $y\left(0^{+}\right)$and $y\left(\infty \right)$ for each of the following transforms. If a theorem does not apply to a particular transform, explain why this is so.

(a)

\[Y(s)=\frac{s^{3}+2 s+4}{s(s+1)^{2}(s+2)}\]

(b)

\[Y(s)=\frac{4 s^{2}+10 s+10}{s^{3}+2 s^{2}+5 s}\]

(c)

\[Y(s)=\frac{3\left(s^{3}+2 s^{2}+4 s+1ight)}{s(s+3)^{2}}\]

(d)

\[Y(s)=\frac{s^{3}-4 s}{(s+1)\left(s^{2}+4 s+4ight)}\]