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Let $\;f , g :R \to R\;$be two functions defined by $\;f(x)=\{ \begin{matrix}x sin(\large\frac{1}{x}) \;, x \neq 0 \\ 0\;,x=0 \end{matrix}\;$ , and $\;g(x)=x f(x)\;$\[\] Statement I : f is a continuous function at x=0 .\[\] Statement II : g is differential function at x=0 .

(a) both statements I and II are false . \[\](b) both statements I and II are true . \[\] (c) statements I is true and statement II is false .\[\](d) statements I is false and statement II is true .
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