If \( \lim _{x \rightarrow \infty}\left([f(x)]+x^{2}\right)\{f(x)\}...

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If \( \lim _{x \rightarrow \infty}\left([f(x)]+x^{2}\right)\{f(x)\}=k \), where \( f(x)=\frac{\tan x}{x} \) and \( [\cdot] \)
\( \mathrm{P} \)
, \{\} denotes greatest integer and fractional part of \( x \)
W respectively, the value of \( [k / e] \) is
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