Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 7 / Solution

For $x>0$, the denominator is positive, so the function graph has the same sign as $\sin x$. Its crossings of the horizontal axis areEach crossing is genuine because the derivative there is $(-1{)}^n/(n\pi {)}^2\ne 0$. Near zero, $\sin x\sim x$, so $y\sim 1/x\to +\infty$; the origin is excluded and is not a crossing. The oscillations alternate sign and decay towards zero as $x\to \infty$, with absolute value at most $1/x^2$.