Let \[g(x)=x.\,f(x),\]where \[f(x)=\left\{ \begin{align} & x\sin \frac – McqOptions

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1.	Let \[g(x)=x.\,f(x),\]where \[f(x)=\left\{ \begin{align} & x\sin \frac{1}{x},\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,0,\,x=0 \\ \end{align} \right.\] at \[x=0\] [IIT Screening 1994; UPSEAT 2004]
A.	g is differentiable but g' is not continuous
B.	g is differentiable while f is not
C.	Both f and g are differentiable
D.	g is differentiable and g' is continuous
Answer» B. g is differentiable while f is not

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