Question

can some one help me to solve this problem step by step?

Use the definitions of O, N, and to prove that: 4n– 12n + 10 = O(n?) 5n5 - 4n4 - 2n+ n = O(n5) 4n2 +n + 1 = 12() nº + n + Zn +1 = en) (5) 13/2 + Vn sin(n) +n log(n) = O(n?) (3)

Answer 1

Ocn) 4n22nt10 = ind 4n2-12n10 <=cn2 Ror Do 2uchthat We nee.d+o Divide both sides n2 4-2t 10 au n-no choose no 29ua to i,-hen we ned a Sueh that 4-12t10 C ogual to B. Now we have Set Con 4n2-1an +10 <= gn2 or au ny1 dinion mdien {(»)i¢ Cge) posilive orslom! c.no 8uch%het So,whove 2 c 3,n1 AC)-12n 10 0(n2/ Provse n4n2n2+n= OCP%) posHivs Sueh that Cors tant no wmeed to ind c and mo 2ueh that - 2n2+n = cn n> =no divid boih 2ide 2 c w chrose neauau n 4, 4hen uo nesd o c guch that we can set c equau Ho . Nou 54 2+ < = c u have -4n1-2n2+n= 0"){(Mraved te-17

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nn3tnn+1 10n Au hore abl to Rind , G= 1, 2=10 ,1 gueh that 0 e 'ntn°+7n + = eC Proved ALnd toind e, no ueh that 3/2 hoth side n2 w put noT, nid e Such that 1to.2414 to < = e Can 3/2 tVD SiT that + Sin (ig O)