L'Hospital's rule.

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How do I show that log^kN is o(N) (small o) for any constant k.
I am so confused with the derivative of log^kN .. i got k (logN) ^ (k-1) but I don't know what to do next.

Lim n→ ∞ log^kN/N

thanks in advance

Posted 1-Feb-11 17:32pm

bowww

Updated 1-Feb-11 17:43pm

m@dhu

v2

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Sergey Alexandrovich Kryukov 1-Feb-11 23:42pm

What do you mean "show". Are you talking about mathematics, Computer Algebra System, presentation of result of symbolic computation, algorithm of approximated calculations (scratch out the unused)?

(There is certain chance you're posting a question to a wrong forum.)

--SA

Sergey Alexandrovich Kryukov 1-Feb-11 23:44pm

As Java is mentioned, you should post your existing Java code and describe what it does properly.

bowww 1-Feb-11 23:47pm

no it's data structures and algorithms i just need to prove that log^kN is small o of (N) using L'Hospital's rule.

Sergey Alexandrovich Kryukov 2-Feb-11 3:17am

What do you mean by proof? L'Hospital already provided a proof...
--SA

bowww 2-Feb-11 3:35am

no i need to show that log^kN is o(N) (small o) for any constant k..

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OriginalGriff · Answer 1 · 2011-02-01T21:19:00

Solution 1

The best suggestion I can give is to have a look at Wolfram Alpha Mathworld: http://mathworld.wolfram.com/LHospitalsRule.html[^] - start here and see what you can find.
If nothing else, it may explain it better than we could because it has all those funny little symbols we only used for APL...

Posted 1-Feb-11 21:19pm

OriginalGriff

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Sergey Alexandrovich Kryukov 2-Feb-11 11:50am

That's good reference, my 5.
Did you understand what OP wants? I have a strong impression that she or he does not understand as well, in hope someone else explains; could be a school assignment. Simple stuff itself, but what's "structures and algorithms" (looks like a chapter from a school plan)? Any idea?
--SA

bowww 2-Feb-11 12:20pm

Well this is a course called data structures and algorithms in java and this question is an assignment question. The course is very difficult and confusing that's why im seeking help.
thanks

Sergey Alexandrovich Kryukov 2-Feb-11 13:51pm

Well, it's seemingly too difficult to you as you still failing to explain your problem.
Let me tell you, from calculus stand point this is one of easiest things, learned not far from the very beginning...
--SA

OriginalGriff 2-Feb-11 14:18pm

I got the "homework" feeling, as well.
Wolfram Alpha is a worthy site - it has a surprisingly good searcher: it can work out what you actually want pretty well even if you don't specify it that well.

Sergey Alexandrovich Kryukov 2-Feb-11 14:49pm

I agree.
Or, do you also mean it could teach OP to understand her or his own questions?
Would be good.

Can I tell you a secret? :-) I developed a new technology for creating Computer Algebra Systems (as a long-ago "hobby"), don't know where to publish it; code's ready. Maybe if I post a question of CodeProject? I don't want to publish on CodeProject because it would close to way to solid journals requiring original publications...
--SA

OriginalGriff 3-Feb-11 3:28am

If you are even thinking of academic publication, then don't post as much as a code fragment on CP: all such are covered by the CP Open Source License (http://www.codeproject.com/info/Licenses.aspx) which would put it into the public domain.
Yes a question about where to publish could work, or phone the IT dept of your nearest / old university?

Sergey Alexandrovich Kryukov 4-Feb-11 2:37am

Thanks for the advice. I understand. Not so easy. If I decide to ask an advice, I'll explain later. Thanks for the tips again.
--SA