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

a) T(n) = T(n-1) + n has solution T(n) = O(n^2)

b)T(n) = T(n/2) + (1) has solution T(n) = O(lg n)

c)T(n) = 2T(n/2) + n has solution T(n) = (lg n)

d)T(n) = 2T(n/2+17) + n has solution T(n) = O(n lg n)

e)T(n) = 2T(n/3) + (n) has solution T(n) = (n)

f)T(n) = 4T(n/2) (n) has solution T(n) = T(n) = (n^2)