How many $x$-intercepts does the graph of $y=\cos(1/x)$ have in the interval $(0.002,0.02)$?

1. $\cos(1/x)=0$ exactly when $\frac1x=\frac\pi2+k\pi=\left(k+\frac12\right)\pi$ for an integer $k\ge0$ (here $x>0$), i.e. $x=\dfrac1{(k+\frac12)\pi}$.
2. We need $0.002<\dfrac1{(k+\frac12)\pi}<0.02$, i.e. $50<\left(k+\frac12\right)\pi<500$, so $\dfrac{50}\pi-\dfrac12
3. This is $15.41\ldots