Question

Select the correct inequality for the asymptotic order of growth of the function n! – 2ⁿ?

1) n! – 2ⁿ = O(n!)
2) n! – 2ⁿ = O(2ⁿ)
3) n! – 2ⁿ = O(n²)
4) n! – 2ⁿ = O(n)

Answer 1

The correct inequality for the asymptotic order of growth of the function n! – 2ⁿ is n! – 2ⁿ = O(2ⁿ).

Step-by-step explanation:

The correct inequality for the asymptotic order of growth of the function n! – 2ⁿ is:

n! – 2ⁿ = O(2ⁿ)

To determine the asymptotic order of growth, we compare the given function with a known function. In this case, we compare it with 2ⁿ, as it has the larger exponent. Since the factorial function grows faster than the exponential function, the correct inequality is n! – 2ⁿ = O(2ⁿ).