The number of $ x$-intercepts on the graph of $ y \equal{} \sin(1/x)$ in the interval $ (0.0001,0.001)$ is closest to

$ \textbf{(A)}\ 2900 \qquad \textbf{(B)}\ 3000 \qquad \textbf{(C)}\ 3100 \qquad \textbf{(D)}\ 3200 \qquad \textbf{(E)}\ 3300$
1. We need to find the number of $x$-intercepts of the function $y = \sin(1/x)$ in the interval $(0.0001, 0.001)$. An $x$-intercept occurs when $y = 0$, which means $\sin(1/x) = 0$.
2. The sine function is zero at integer multiples of $\pi$, so we need $1/x = k\pi$ for some integer $k$. Solving for $x$, we get $x = \frac{1}{k\pi}$.
3. We need to find the values of $k$ such that $x = \frac{1}{k\pi}$ lies within the interval $(0.0001, 0.001)$. This gives us the inequality:
   \[
   0.0001 \leq \frac{1}{k\pi} \leq 0.001
   \]
4. Taking the reciprocal of the inequality (and reversing the inequality signs), we get:
   \[
   1000 \leq k\pi \leq 10000
   \]
5. Dividing through by $\pi$, we obtain:
   \[
   \frac{1000}{\pi} \leq k \leq \frac{10000}{\pi}
   \]
6. Using the approximation $\pi \approx 3.14159$, we calculate:
   \[
   \frac{1000}{\pi} \approx \frac{1000}{3.14159} \approx 318.31
   \]
   \[
   \frac{10000}{\pi} \approx \frac{10000}{3.14159} \approx 3183.1
   \]
7. Therefore, $k$ must be an integer in the range $318 \leq k \leq 3183$. The number of integers in this range is:
   \[
   3183 - 318 + 1 = 2866
   \]
8. Since the closest answer to 2866 is 2900, we conclude that the number of $x$-intercepts is closest to 2900.

The final answer is $\boxed{2900}$