Testwiki:Reference desk/Archives/Mathematics/2016 July 24

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July 24

Sine Function

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

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

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

Order of Growth

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

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

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

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