Hi didn't really know where this belongs so here goes...

show that $\displaystyle log_eN^c=O(N) \forall c \in \mathbb{R}\setminus{0}$

and

find O(f(x)) for $\displaystyle f(x) = x^4 + 2^x + log_en$

Thanks a lot for the help all=)

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- Aug 1st 2010, 04:04 PMjames12Big O examples
Hi didn't really know where this belongs so here goes...

show that $\displaystyle log_eN^c=O(N) \forall c \in \mathbb{R}\setminus{0}$

and

find O(f(x)) for $\displaystyle f(x) = x^4 + 2^x + log_en$

Thanks a lot for the help all=) - Aug 1st 2010, 08:46 PMCaptainBlack
$\displaystyle \log(N^c)=c\log(N)$

Then as $\displaystyle \log(N) \in O(N)$, so is $\displaystyle c\log(N)$.

If you need to prove that: $\displaystyle \log(N) \in O(N)$

you use L'Hopital's rule to show that:

$\displaystyle \displaystyle \lim_{N \to \infty} \frac{\log(N)}{N}=0$

and the result follows from that.

CB - Aug 1st 2010, 08:49 PMCaptainBlack
- Aug 2nd 2010, 01:30 AMjames12
Thanks so much CaptainBlack, life saver=) =)