Question

Using the definition of the Big-Oh asymptotic notation, show that

                                             10? = ?( n² )

Answer 1

we say, f(n) = O(g(n)) if and only if there exists a positive real number C and a real number n0 such that
|f(n)| <= C * |g(n)| for all n > n0

10*n = O(n^2)

10*n   <= C * n^2
10     <= C * n

Above statement is true for C = 1 and n >= 10

so, !0n = O(n^2) for C = 1 and n0 = 10