Question

Let f, g: Z+ →R, where f (n) _ n^2 + n and g(n) = (1/2) n^3, for n ∈ Z+

Answer 1

ok

Answer 2

Here is what I have for my answer
For all n ∈ Z+
, 0 ≤ log2 n < n. So let k _ 1 and m _ 200 in Definition 5.23. Then
|f (n)| _ 100 log2 n _ 200
_ 1
2 log2 n
_
< 200
_ 1
2n
_
_ 200|g(n)|, so f ∈ O(g).
b) For n _ 6, 2n _ 64 < 3096 _ 4096 − 1000 _ 212 − 1000 _ 22n − 1000. Assuming that
2k < 22k − 1000 for n _ k ≥ 6, we find that 2 < 22 ⇒2(2k) < 22(22k − 1000) < 2222k − 1000,
or 2k+1 < 22(k+1) − 1000, so f (n) < g(n) for all n ≥ 6. Therefore, with k _ 6 and m _ 1 in

Answer 3

Just want to make sure that is the right answer

Answer 4

ok
but what was the question?

Answer 5

Let f, g: Z+ →R, where f (n) _ n^2 + n and g(n) = (1/2) n^3, for n ∈ Z+

Answer 6

hold on
Let f, g: Z+ →R, where f (n) =n^2 + n and g(n) = (1/2) n^3, for n ∈ Z+

Answer 7

for some reason it did not want to put the = in the problem

Answer 8

@satellite73 @amistre64 @phi @Mertsj