Provide an asymptotic runtime complexity of each recurrence using Big O Notation. For these

recurrences, do not directly use the Master Theorem to find the asymptotic time complexity $($i$.$e$.$

do not plug in values of $a,b,d$ directly into the Master Theorem to find the Big O time complexity$).$

Make sure to show your work in order to justify your answer!

$($a$)T(n)=8T(\frac{n}{2})+n$

$($b$)T(n)=2T(\frac{n}{4})+T(\frac{n}{2})+n$

$($c$)T(n)=4T(n-1)+1$