July 24

Hi, is that true that ${\displaystyle \alpha \cdot \sin(\beta x)}$ is ${\displaystyle {\frac {2\pi }{\beta }}}$-periodic (for every ${\displaystyle \alpha }$)? 31.154.81.45 (talk) 05:57, 24 July 2016 (UTC)[reply]

Yes. The constant factor α makes no difference to the periodicity. —Tamfang (talk) 06:28, 24 July 2016 (UTC)[reply]

Thank you! 80.246.138.78 (talk) 09:07, 24 July 2016 (UTC)[reply]

What is the order of growth (=big-O notation, or Theta-notation), of ${\displaystyle e^{i\theta }}$ as ${\displaystyle \theta }$ tends to zero? 185.32.179.12 (talk) 12:05, 24 July 2016 (UTC)[reply]

O(1). In fact, ${\displaystyle \lim _{\theta \to 0}e^{i\theta }=1}$. Sławomir Biały (talk) 12:22, 24 July 2016 (UTC)[reply]

Thanks :) 31.154.81.45 (talk) 10:16, 25 July 2016 (UTC)[reply]

Would it help to mention that ${\displaystyle e^{i\theta }\approx 1+i\theta }$ in that neighborhood? —Tamfang (talk) 06:38, 26 July 2016 (UTC)[reply]