Consider two recurrence relations P$($n$)=2$P$($n$/2)+$ n and Q$($n$)=4$Q$($n$/4)+2$n$.$ What is the

relationship between P and Q$?$ Is P $=$ O$($Q$),$ P $=($Q$),$ or P $=\backslash$Theta $($Q$)?$ Prove your answer

using limit of ratio definition of asymptotic notations