If \[f(x)=\left\{ \begin{align} & x\sin \frac{1}{x},\ \ \ \ \ x\ne 0 \\ & \ \ \ \ \ \ 0,\ \ \ \ \ x=0 \\ \end{align} \right.\], then \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\] [IIT 1988; MNR 1988; SCRA 1996; UPSEAT 2000, 01]

If \[f(x)=\left\{ \begin{align} & x\sin \frac{1}{x},\ \ \ \ \ x\ne

1.	If \[f(x)=\left\{ \begin{align} & x\sin \frac{1}{x},\ \ \ \ \ x\ne 0 \\ & \ \ \ \ \ \ 0,\ \ \ \ \ x=0 \\ \end{align} \right.\], then \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\] [IIT 1988; MNR 1988; SCRA 1996; UPSEAT 2000, 01]
A.	1
B.	0
C.	?1
D.	None of these
Answer» C. ?1

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If \[f(x)=\left\{ \begin{align} & x\sin \frac{1}{x},\ \ \ \ \ x\ne 0 \\ & \ \ \ \ \ \ 0,\ \ \ \ \ x=0 \\ \end{align} \right.\], then \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\] [IIT 1988; MNR 1988; SCRA 1996; UPSEAT 2000, 01]

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