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

• Jun 9th 2009, 11:28 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.

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