Let f : ℝ → ℝ be a function defined by
\(f(x)=\left\{\begin{array}{cc} x^{2} \sin \left(\frac{\pi}{x^{2}}\right), & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right.\)
Then which of the following statements is TRUE?
1
f(x) = 0 has infinitely many solutions in the interval \(\left[\frac{1}{10^{10}}, \infty\right)\).
2
f(x) = 0 has no solutions in the interval \(\left[\frac{1}{\pi}, \infty\right)\).
3
The set of solutions of f(x) = 0 in the interval \(\left(0, \frac{1}{10^{10}}\right)\) is finite.
4
f(x) = 0 has more than 25 solutions in the interval \(\left(\frac{1}{\pi^{2}}, \frac{1}{\pi}\right)\).