Can you spell the name of this function?

Calculus Level 5

Let \( \omega(x) = \displaystyle \sum_{n=0}^{\infty} \dfrac{1}{2^{n}} \sin\left(2^{n}x \right) \).

Evaluate \( \displaystyle \lim_{h\rightarrow 0} \dfrac{\omega(x+h)-\omega(x)}{h}\) at \(x=2016^{\circ} \).

If the answer cannot be inputted into the solution box, select the correct option below and input the number of the option that best fits the correct answer:

  • Limit DNE, by approaching \( + \infty\) on both sides of 2016: Input 1234

  • Limit DNE, by approaching \( - \infty \) on both sides of 2016: Input 4321

  • Limit DNE, by not approaching the same value from left and from right of 2016, but not approaching \(\pm \infty\) on either side: Input 1324

  • Limit DNE, by approaching \( -\infty \) from the left of 2016, and \(+ \infty\) from the right of 2016: Input 1243

  • Limit DNE, by approaching \( +\infty \) from the left of 2016, and \( - \infty \) from the right of 2016: Input 3241

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