Find set of values of x for which limit = 0?

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June 9th 2009, 10:28 PM
fardeen_gen

Find set of values of x for which limit = 0?

If $\lim_{n\rightarrow \infty} \frac{1}{\left(\frac{3}{\pi} \arctan 2x\right)^{2n} + 5} = 0$ , then find the set of values of x.

Answer:

Spoiler:

$x\in \left(-\infty, -\frac{\sqrt{3}}{2}\right) \cup \left(\frac{\sqrt{3}}{2}, \infty\right)$

How to do it?
June 10th 2009, 12:49 AM
Ruun

You want the absolute value of $\left(\frac{3}{\pi} \arctan 2x\right)^{2n}>1$ see why?

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