# Homework Solution: Explanation and some work please. Please use L'Hôpital's Rule for the exlpanation and work….

Explanation and some work please. Please use L'Hôpital's Rule for the exlpanation and work. For each of the following pair of functions f(n) and g(n), decide if f(n) = O (g(n), or g(n) = O(f(n)), and explain. (1) f(n) = 2^n, g(n) = n^log n (2) f(n) = squareroot n, g(n) = (log n)^2 (3) f(n) = n^1/3, g(n) = n/log n (4) f(n) = n^3 + 2n^2 + 10n, g(n) = 100 n^2 (5) f(n) = (log n)^3 + 5 log n, g(n) = n

Explanation and some effort content. Content portraiture L’Hôpital’s Rule coercion the exlpanation and effort. Coercion each of the subjoined couple of functions f(n) and g(n), career if f(n) = O (g(n), or g(n) = O(f(n)), and elucidate. (1) f(n) = 2^n, g(n) = n^log n (2) f(n) = squareroot n, g(n) = (log n)^2 (3) f(n) = n^1/3, g(n) = n/log n (4) f(n) = n^3 + 2n^2 + 10n, g(n) = 100 n^2 (5) f(n) = (log n)^3 + 5 log n, g(n) = n

## Expert Exculpation

1) f(n) > g(n) , hereafter g(n) = O(f(n))

2. f(n) > g(n) , hereafter g(n) = O(f(n)) 3. g(n) > f(n), hereafter f(n) = O(g(n)) 4: as f(n) has the max promise as n^3 and g(n) is of regulate n^2, hereafter f(n) > g(n), hereafter g(n) = O(f(n))

5. g(n) > f(n), hereafter f(n) = O(g(n)) 