If \[f(x)=\left\{ \begin{align} & \frac{x-|x|}{x},\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,2,\,\text{when}\,x=0 \\ \end{align} \right.\], then [AI CBSE 1982]

\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=2\]

\[f(x)\]is continuous at \[x=0\]

\[\left[ 0,\frac{\pi }{2} \right]\]is discontinuous at \[x=0\]

If \[f(x)=\left\{ \begin{align} & \frac{x-|x|}{x},\text{when}\,x\ne

1.	If \[f(x)=\left\{ \begin{align} & \frac{x-\|x\|}{x},\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,2,\,\text{when}\,x=0 \\ \end{align} \right.\], then [AI CBSE 1982]
A.	\[f(x)\]is continuous at \[x=0\]
B.	\[\left[ 0,\frac{\pi }{2} \right]\]is discontinuous at \[x=0\]
C.	\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=2\]
D.	None of these
Answer» C. \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=2\]

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If \[f(x)=\left\{ \begin{align} & \frac{x-|x|}{x},\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,2,\,\text{when}\,x=0 \\ \end{align} \right.\], then [AI CBSE 1982]

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