If \( f(x)=x^{2} \cdot \sin (1 / x), x \neq 0 \) and \( f(0)=0 \) then, (A) \( f(x) \) is contin...

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If \( f(x)=x^{2} \cdot \sin (1 / x), x \neq 0 \) and \( f(0)=0 \) then,
(A) \( f(x) \) is continuous at \( x=0 \)
\( \mathrm{P} \)
(B) \( f(x) \) is derivable at \( x=0 \)
VW
(C) \( \mathrm{f}^{\prime}(\mathrm{x}) \) is continuous at \( x=0 \)
(D) \( \mathrm{f}^{\prime}(\mathrm{x}) \) is not derivable at \( \mathrm{x}=0 \)
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