\[f(x)=\left\{ \begin{matrix} \frac{x}{2{{x}^{2}}+\left| x \right|,}\,\,x\ne 0 \\ 1.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]. Then \[f(x)\] is

continuous but non-differentiable at x=0

\[f(x)=\left\{ \begin{matrix} \frac{x}{2{{x}^{2}}+\left| x \right|,}\

1.	\[f(x)=\left\{ \begin{matrix} \frac{x}{2{{x}^{2}}+\left\| x \right\|,}\,\,x\ne 0 \\ 1.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]. Then \[f(x)\] is
A.	continuous but non-differentiable at x=0
B.	differentiable at x=0
C.	discontinuous at x=0
D.	none of these
Answer» D. none of these

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\[f(x)=\left\{ \begin{matrix} \frac{x}{2{{x}^{2}}+\left| x \right|,}\,\,x\ne 0 \\ 1.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]. Then \[f(x)\] is

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