Prove that the function \( f \) defined by \( \mathrm{P} \) \[ f(x)...

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Prove that the function \( f \) defined by
\( \mathrm{P} \)
\[
f(x)=\left\{\begin{array}{ll}
\frac{x}{|x|+2 x^{2}}, & x \neq 0 \\
k, & x=0
\end{array}\right.
\]
W.
remains discontinuous at \( x=0 \), regardless the choice of \( k \).
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