# Changes

| [[horizontal asymptote]]s || $y = 0$, i.e., the $x$-axis. This is because $\lim_{x \to \pm \infty} \frac{\sin x}{x} = 0$, which in turn can be deduced from the fact that the numerator is bounded while the magnitude of the denominator approaches $\infty</matH>. |- | [[local maximum value]]s and points of attainment || The local maxima occur at points [itex]x$ satisfying $\tan x = x$ and $x \in [2n\pi,(2n + 1)\pi]$ or $x \in [-(2n + 1)\pi,-2n\pi]$ for $n$ a positive integer.<br> There is an anomalous local maximum at $x = 0$ with value 1. Apart from that, the other local maxima occur at points of the form $\pm(2n\pi + \alpha_n)$ where $\alpha_n$ is fairly close to $\pi/2$ for all $n > 0$. The local maximum value at this point is slightly more than $1/(2n\pi + \pi/2)$.
| [[local minimum value]]s and points of attainment || The local minima occur at points $x$ satisfying $\tan x = -x$ and $x in [(2n - 1)\pi,2n\pi]$ or $x \in [-2n\pi,-(2n - 1)\pi]$ for $n$ a positive integer.<br> The local minima occur at points of the form $\pm(2n\pi - \alpha_n)$ where $\alpha_n$ is fairly close to $\pi/2$ for all $n > 0$. The local minimum value at this point is slightly less than $-1/(2n\pi - \pi/2)$.