4. 5. (a) Find suitable values of M1, M2, M3, M4 € N, so that the following inequalities are true. Use algebraic manipu-

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4 5 A Find Suitable Values Of M1 M2 M3 M4 N So That The Following Inequalities Are True Use Algebraic Manipu 1 (90.66 KiB) Viewed 25 times

4. 5. (a) Find suitable values of M1, M2, M3, M4 € N, so that the following inequalities are true. Use algebraic manipu- lations of the inequalities and some of the rules in Prac class 8B. (i) 7 < žn2 is true for n > M1 (ii) 4 log2 (n) < žn_ is true for n > M2 (iii) 14n < în2 is true for n > M3 (iv) 6n log2 (n) < nis true for n > M4 (b) Find a value M E N such that the four inequalities in part (a) hold simultaneously for n > M. (c) Use your answers to (a) and (b) to prove that 1 14 n? +6n log2 (n) + En +4 log2 (n) +7 € O(n?), with c = 3. 3 9 .2