# Thread: Big O notation check

1. ## Big O notation check

Have I worked through this correctly ?

$\displaystyle f(x) = x^3+2x^2-x+2$
$\displaystyle |f(x)| = |x^3+2x^2-x+2|$
$\displaystyle <= |x^3|+2|x^2| +|x|+|2|$ by triangle inequality
$\displaystyle = x^3+2x^2+x+2 \text{ if } x >= 0$

$\displaystyle <= x^3+2x^3+x^3+2x^3$ <--is this last 2x^3 ok?
$\displaystyle = 6x^3$

therefore $\displaystyle f(x) = O(x^3)$

Thanks for any help

2. Originally Posted by dunsta
Have I worked through this correctly ?

$\displaystyle f(x) = x^3+2x^2-x+2$
$\displaystyle |f(x)| = |x^3+2x^2-x+2|$
$\displaystyle <= |x^3|+2|x^2| +|x|+|2|$ by triangle inequality
$\displaystyle = x^3+2x^2+x+2 \text{ if } x >= 0$

$\displaystyle <= x^3+2x^3+x^3+2x^3$ <--is this last 2x^3 ok?
$\displaystyle = 6x^3$

therefore $\displaystyle f(x) = O(x^3)$

Thanks for any help
Line 5 requires you take x>=1, but otherwise yes.

CB

3. Things take a darker turn in the last few episodes, especially since Paradigm City's strange past becomes the most important part. Roger is hired to give a severance check to Schwarzwald, but becomes enmeshed in his plans for Paradigm City -- and witnesses the unveiling of another Megadeus, Big Duo.

And when a series of murders are committed by a red-cloaked figure -- who leaves Big O's motto "Cast In The Name of God, Ye Not Guilty" at each crime -- Roger starts to suspect that Dorothy may be involved. And even more confusing, Roger is suffering flashbacks of whatever happened forty years ago... which may be even more ghastly than anyone suspects.

"The Big O" is one of those series that drips with lots of influences -- it hasa lovely classic noir feeling, more than a hint of "Batman," and some tinges of Isaac Asimov (R. Dorothy?). And even the animation has a style reminiscent of art deco, with lots of long clean lines and dark shapes -- even the vast Megadeuses and other mecha have them.
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Ben 10 Games