Use the substitution method to show that each of the following recurrences de- fined on the reals has the asymptotic solution specified:

(a) T(n)=T(n1)+n has solution T(n)=O(n2). (b) T(n)=T(n/2)+(1) has solution T(n)=O(logn) (c) T(n)=2T(n/2)+n has solution T(n)=(nlogn) (d) T(n)=2T(n/3)+(n) has solution T(n)=(n) (e) T(n)=2T(n/2+17)+n has solution T(n)=O(nlogn)