Question $4$:$10$ points

Consider two recurrence relations $P(n)=2P(\frac{n}{2})+n$ and $Q(n)=4Q(\frac{n}{4})+2n.$ What is the

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

using limit of ratio definition of asymptotic notations.