# 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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