Let $f, g: R \to R$ be two functions defined by $f(x) = \begin{cases} x \sin \left( \frac{1}{x} \right), & x \ne 0 \\ 0, & x = 0 \end{cases}$ and $g(x) = x f(x)$.
Statement $I$: $f$ is a continuous function at $x = 0$.
Statement $II$: $g$ is a differentiable function at $x = 0$.
Statement $I$: $f$ is a continuous function at $x = 0$.
Statement $II$: $g$ is a differentiable function at $x = 0$.
- ABoth statement $I$ and $II$ are false.
- BBoth statement $I$ and $II$ are true.
- CStatement $I$ is true,statement $II$ is false.
- DStatement $I$ is false,statement $II$ is true.
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