Question

4. Select a theta notation chosen from Olign) , O(n), O(nlgn), o(na), O(nk) If your answer is o link), specify the Constant k. a) 2n?+!. b) 3 n²+ anlgn c). 6n6 +n+4 d) 2+4 +6+un+an e) (6n +4) (1 + Ign) - Type here to search o A e - a

Answer 1

ca) 2071 ant1 = 257n² (for n=1) ant & 3n2 let C1-3, by definition & o, 2571 = 0 (7) Also, 2571 220 (fos 121) let Ca=2, by definition of I, 22 7 1 = 12 (7) C13, C2 = 2, 2017) (b) 35 + 20egn 307 2ndgn – 307+2 m² (formal) - 5n² let C1-5, by definition of 0, 35+201gn=0(%) Also, 3+2n dgn s 3n2 (for 231) let (2=3, by def of 2, 3nt 2nign=(n)! CIES,C2-3 cm)

(6) 658+n+4 En tnty a botn + 406 (for m2). let Ca= 11, by def. g 0, 6n+n+y = 0 Gunty = 64 (for n=1) let (2=6, by def of er, snenty = 2(n) c=11, c2=6 , o (no) k=6] (d) 2+ 4 + 6+ ... +29 = n(n+1) - in vrne ntn? (for n? 1). <2n? eet c1=2, & niin = o(r) nithan (for n? 1) let (2=1 ntn 2 (²) C1= 2, c2=1. OCNP)

re (6nty) (Itegn) fm = 6nt bn lgn + 4 lgnty tin) = bn gn + bulgn + unegntungn (for 121) I s innen eet C=17, find- ocnlgn) f(n) = 6negn (fes n21) let 2-6 , fore(nlgn) 0,= 17, 2-6, o (nn)
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