1. The problem asks to find the limit $$\lim_{x \to 0} \sin\left(\frac{\pi}{x}\right)$$ given that $$f(0.001) = f(0.0001) = 0$$ where $$f(x) = \sin\left(\frac{\pi}{x}\right)$$. 2. The function $$\sin\left(\frac{\pi}{x}\right)$$ oscillates between -1 and 1 infinitely many times as $$x$$ approaches 0 because $$\frac{\pi}{x}$$ becomes very large in magnitude. 3. Although $$f(0.001) = 0$$ and $$f(0.0001) = 0$$, these are just two points where the sine function hits zero. The sine function will also take all values between -1 and 1 infinitely often near 0. 4. Therefore, the limit $$\lim_{x \to 0} \sin\left(\frac{\pi}{x}\right)$$ does not exist because the function does not approach a single value. 5. In summary, the limit does not exist due to infinite oscillations near zero. Final answer: $$\lim_{x \to 0} \sin\left(\frac{\pi}{x}\right) \text{ does not exist}.$$