I have a fair idea of what Big-O Notation is, but I'd like to know if there's a sure fire way to calculate the values of C and k for which
Example question:
Via trial and error, I have found them out to be C = 4, k = 9. Is there a specific method to calculate these values?
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$\begingroup$Is there a specific method to calculate these values?
No.
In the case you explain though, for every $x\geqslant1$, $x^4+9x^3+4x+7\leqslant x^4+9x^4+4x^4+7x^4$ hence $k=1$ and $C=21$ fit.
Likewise (exercise), $k=2$ and $C=7$ would fit. Or $k=5$ and $C=4$. Or many others.
$\endgroup$ 2 $\begingroup$There is no specific general method to calculate these values. In this case you could fix any $C$ greater than $1$ and then determine a $k$ via solving the resulting (in)equality.
However, please note that the point here is not at all to find optimal values; basically you can take whathever works conveniently. Normally, one uses this asymptotic notation precisely when one does not care about the fine details but just wants a rough idea.
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