Question

Show formally that the following relation is correct. Give the values of constants c and n₀.

n²logn = $\Omega$ (n²+100)

Answer 1

"Big omega notation: - Consider a function g(n), we define Ohm g(n) as Ohm (g(n)) = {f(n): I positive constants can d n_0, such that Forall n greaterthanorequalto n_0 we have 0 lessthanorequalto c g(n) lessthanorequalto f(n)} It is simply referred as. ""Asymptotic notation greater than or equal to"" f(n) greaterthanorequalto (n). \r\n n^2 log n = Ohm (n^2 + 100) Here f(n) = n^2 log n g(n) = n^2 + 100 and c = 1 n^2 log n greaterthanorequalto n^2 + 100 Let n_0 = 19 19^2 log 19 greaterthanorequalto 19^2 + 100 361 times 1.28 greaterthanorequalto 361 + 150 462 Partialdifferential 461 Therefore n_0 = 19 and c = 1"