I want to write these two in the big O notation: (it's $h\rightarrow0$)

  1. $f(h)=\sqrt{h^3}$

  2. $f(h)=h\cdot \log h $

But I don't have any idea how to do this.

Thanks for helping!


What you ask makes no sense, really. You have two functions; they are fine as they stand, no big O is needed to understand them. Big O is a notation to related a given function to something else, presumably simpler, or just to write an estimate in a form where you don't want to bother with the implied constants. You could certainly write $\sqrt{h^3}=O(h)$, for example, but if it makes sense to do so depends on context. Ditto for the other one, which is (among many things) $h\cdot\log(h)=O(h^{1+\varepsilon})$ for any $\varepsilon>0$. But again, whether it makes sense to write it so depends on context.


I don't really why $h\rightarrow 0$, i use this notation when $h\rightarrow\infty$ for look the complexity of algorithm. So, may be you want to use a substitution with $u=1/h$ and see it like me.

  1. $O(h^{1/3})$

  2. $O(n\cdot \log n)$ look that is Big O, is like that Complexity for Quicksort Algorithm in the average case.

Big-O is for me like a function boundary for the function and take the most important for the result function. Then, we forget things like coefficient constants. For Example: $O(4x^4+ x^2)=O(4x^4)= O(x^4)$



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.