For the function \[f(x)=\left\{ \begin{align} & \frac{{{e}^{1/x}}-1}{{{e}^{1/x}}+1},\,\,x\ne 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,x=0 \\ \end{align} \right.\], which of the following is correct [MP PET 2004]

\[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]does not exist

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

\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=1\]

\[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]exists but \[f(x)\]is not continuous at \[x=0\]

For the function \[f(x)=\left\{ \begin{align} & \frac{{{e}^{1/x}}-1

1.	For the function \[f(x)=\left\{ \begin{align} & \frac{{{e}^{1/x}}-1}{{{e}^{1/x}}+1},\,\,x\ne 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,x=0 \\ \end{align} \right.\], which of the following is correct [MP PET 2004]
A.	\[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]does not exist
B.	\[f(x)\]is continuous at \[x=0\]
C.	\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=1\]
D.	\[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]exists but \[f(x)\]is not continuous at \[x=0\]
Answer» E.

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For the function \[f(x)=\left\{ \begin{align} & \frac{{{e}^{1/x}}-1}{{{e}^{1/x}}+1},\,\,x\ne 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,x=0 \\ \end{align} \right.\], which of the following is correct [MP PET 2004]

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