If \[f(x)=\left\{ \begin{align} & x\frac{{{e}^{(1/x)}}-{{e}^{(-1/x)}}}{{{e}^{(1/x)}}+{{e}^{(-1/x)}}},\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,x=0 \\ \end{align} \right.\] then which of the following is true [Kurukshetra CEE 1998]

f is differentiable at every point

f is continuous and differentiable at every point

f is continuous at every point but is not differentiable

f is differentiable only at the origin

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

1.	If \[f(x)=\left\{ \begin{align} & x\frac{{{e}^{(1/x)}}-{{e}^{(-1/x)}}}{{{e}^{(1/x)}}+{{e}^{(-1/x)}}},\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,x=0 \\ \end{align} \right.\] then which of the following is true [Kurukshetra CEE 1998]
A.	f is continuous and differentiable at every point
B.	f is continuous at every point but is not differentiable
C.	f is differentiable at every point
D.	f is differentiable only at the origin
Answer» C. f is differentiable at every point

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If \[f(x)=\left\{ \begin{align} & x\frac{{{e}^{(1/x)}}-{{e}^{(-1/x)}}}{{{e}^{(1/x)}}+{{e}^{(-1/x)}}},\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,x=0 \\ \end{align} \right.\] then which of the following is true [Kurukshetra CEE 1998]

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