Indicate a range of roots of $\epsilon x \tan(x)=1$ for which it is impossible to get an approximation using expansions.
Since $\epsilon$ is small, I think for the equation to hold, we need either $x \to \infty$ or $x=k \pi+\pi/2$.
I think the root $x \to \infty$ may be the root the problem is looking for. Since $tan(x)$ is oscillating in infinity. I am not sure if this is right and I am having trouble to justify it.
Could someone kindly help? Thanks!