# Infinite crossings

**Calculus**Level 4

Let \(x_n\) be the \(n^{th}\) zero-crossing of the function \(f(x)\), where \(x_1 = \dfrac{1}{\pi}\), and \(x_2 = \dfrac{1}{2\pi}\) and so on in the negative direction. Also let \(f'(x)=\dfrac{df(x)}{dx}\).

Find \(\displaystyle \lim_{n \to \infty} \frac{f'(x_{n+1})}{f'(x_n)}\)