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Cormen Edition 3 Exercise 4.5 Question 3 (Page No. 97)

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Cormen Edition 3 Exercise 4.5 Question 5 (Page No. 97)
Consider the regularity condition $af(n/b) \leq cf(n)$ for some constant $c<1$,which is part of case 3 of the master theorem. Give an example ... satisfies all the conditions in case 3 of the master theorem except the regularity condition.
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Cormen Edition 3 Exercise 4.5 Question 4 (Page No. 97)
Can the master method be applied to the recurrence $T(n)=4T(n/2)+n^2\ lg\ n$ ?Why or why not? Give an asymptotic upper bound for this recurrence.
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Cormen Edition 3 Exercise 4.5 Question 2 (Page No. 97)
Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen's algorithm. His algorithm will use the ... Caesar's algorithm would be asymptotically faster than Strassen's algorithm?
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Cormen Edition 3 Exercise 4.6 Question 3 (Page No. 106)
Show that case 3 of the master theorem is overstated, in the sense that the regularity condition $af(n/b)\geq cf(n)$ for some constant $c<1$ implies that there exists a constant $\epsilon >0$ such that $f(n)=\Omega(n^{log_ba+\epsilon})$.
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