# What is the limit of arccos((1+x^2)/(1+2x^2)) as x goes to infinity?

$\frac{\pi}{3}$
$\arccos \left(\frac{1 + {x}^{2}}{1 + 2 {x}^{2}}\right) = \arccos \left(\frac{\frac{1}{{x}^{2}} + 1}{\frac{1}{x} ^ 2 + 2}\right)$.
Now apply the limit $x \to \infty$, it would be $\arccos \left(\frac{1}{2}\right) = \frac{\pi}{3}$