If 2 functions each big $\mathcal O$ of each other, then place them on the same level. $x^2 + x^3, 3^x, x!, x \log(x), x^2 + 2^x, 2^{x \log(x)}, \log(x^2), 6 \log(x), 2^x, x(1+2+\dots+x)$

My answer is:

$x(1+2+· · ·+x) = x(x(x+1))/2 = x(x^2+x)/2 = (x^3+x^2)/2$

The list is:

$x^2+x^3, \mathcal O((x^3+x^2)/2)$

$3^x, 2^x$

$x \log(x), \mathcal O(2^{x \log(x)})$

$6 \log(x), \log(x^2) = 2 \log x$

$x^2 + 2^x$


Is this correct? Do I need to mention $\mathcal O(....)$ in my answer or can I remove the $\mathcal O$?

  • 2
    $\begingroup$ Please use MathJax it hurts my eyes $\endgroup$ – Peter Foreman Apr 21 at 22:55
  • $\begingroup$ Is there supposed to be a comma between $x!$ and $x\log(x)$ in your list? $\endgroup$ – Neil A. Apr 22 at 2:39
  • $\begingroup$ yes..................... $\endgroup$ – ionics Apr 22 at 2:52

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