MCQ
If $\begin{gathered} f(x)\, = \,\left\{ \begin{gathered}
x\left( {\frac{{{e^{1/x}} - {e^{ - 1/x}}}}{{{e^{1/x}} + {e^{ - 1/x}}}}} \right)\,,\,\,x \ne 0 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,x\, = \,0\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\
\end{gathered} \right. \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ \hfill \\
\end{gathered}$ then correct statement is
x\left( {\frac{{{e^{1/x}} - {e^{ - 1/x}}}}{{{e^{1/x}} + {e^{ - 1/x}}}}} \right)\,,\,\,x \ne 0 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,x\, = \,0\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\
\end{gathered} \right. \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ \hfill \\
\end{gathered}$ then correct statement is
- A$f$ is continuous at all points except $x = 0$
- ✓$f$ is continuous at every point but not differentiable
- C$f$ differentiable at every point
- D$f$ is differentiable only at the origin