Derive asymptotic upper and lower bounds for T$($n$)$ using the methods

specified for the following recurrences. Assume that T$($n$)$ is constant for small

values of n$.$ Provide tight bounds, along with a justification. If the recurrence is

not solvable using the given method, explain why.

i$.$ Solve T$($n$)=4$T$($n$/8)+$ n$4$ using the substitution method.

ii$.$ Analyze T$($n$)=5$T$($n$/8)+$ k$.$n$4$ using the recursion tree method.

iii. Apply the master$$s theorem to solve T$($n$)=4$T$($n$/2)+2$n$.$