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