Question

Let $f:\R→\R$ be a function defined by
$f(x) = \begin{cases} x^2\sin(\frac{\pi}{x^2}), & \text{if } x \ne 0, \\\ 0, & \text{if } x = 0. \end{cases}$
Then which of the following statements is TRUE ?

• A. f(x) = 0 has infinitely many solutions in the interval $[\frac{1}{10^{10}},\infin)$
• B. f(x) = 0 has no solutions in the interval $[\frac{1}{\pi},\infin).$
• C. The set of solutions of f(x) = 0 in the interval $(0,\frac{1}{10^{10}})$ is finite.
• D. f(x) = 0 has more than 25 solutions in the interval $(\frac{1}{\pi^2},\frac{1}{\pi})$

Answer 1

Answer: (D)

f(x) = 0 has more than 25 solutions in the interval $(\frac{1}{\pi^2},\frac{1}{\pi})$

Answer 2

The correct option is (D):f(x) = 0 has more than 25 solutions in the interval $(\frac{1}{\pi^2},\frac{1}{\pi})$.