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The value of $\lim _{x \rightarrow 0^{+}} \frac{x}{p}\left[\frac{q}{x}\right]$ is
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Verified Answer
The correct answer is:
$\frac{[q]}{p}$
$$
\begin{aligned}
&\text { Given, } \lim _{x \rightarrow 0^{+}} \frac{x}{p}\left[\frac{q}{x}\right]\\
&\begin{array}{l}
=\lim _{x \rightarrow 0^{+}} \frac{x}{p}\left(\frac{q}{x}-\{\frac{q}{x}\right\}\right) \\
=\frac{[q]}{p}-\frac{x}{p}\left\{\frac{q}{x}\right\} \\
=\frac{[q]}{p}-0=\frac{[q]}{p}
\end{array}
\end{aligned}
$$
\begin{aligned}
&\text { Given, } \lim _{x \rightarrow 0^{+}} \frac{x}{p}\left[\frac{q}{x}\right]\\
&\begin{array}{l}
=\lim _{x \rightarrow 0^{+}} \frac{x}{p}\left(\frac{q}{x}-\{\frac{q}{x}\right\}\right) \\
=\frac{[q]}{p}-\frac{x}{p}\left\{\frac{q}{x}\right\} \\
=\frac{[q]}{p}-0=\frac{[q]}{p}
\end{array}
\end{aligned}
$$
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