Question

Select the correct inequality for the asymptotic order of growth of the function n² – nlogn?

1) n² = Θ(nlogn)
2) n² = Θ(n³)
3) n² = Θ(logn)
4) n² = Θ(n)

Answer 1

The correct inequality for the asymptotic order of growth of the function
`n² - nlogn is Θ(n²)`, because the
`n²` term is the dominant term and determines the overall growth rate.

Step-by-step explanation:

When analyzing the asymptotic order of growth of a function, we are interested in understanding how the function behaves as the input size becomes very large. To do this, we often use Big Theta notation (Θ) to describe tight bounds on the growth rate of the function. Looking at the function
`n² - nlog(n), the n²` term dominates the growth since, as n becomes very large, the
`n²` term increases much faster than the nlog(n) term. Therefore, we can say that
`n² - nlog(n)`is in
`Θ(n² ).`