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  4. The value of lim limitsx → 0+ (x/p)[(q/x)] is

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Q. The value of $\lim\limits_{x \to 0+} \frac{x}{p}\left[\frac{q}{x}\right]$ is

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Solution:

$\lim\limits_{x \to 0^+} \frac{x}{p}\left(\frac{q}{x}-\left\{\frac{q}{x}\right\}\right) = \lim\limits_{x \to 0^+} \frac{q}{p} - \lim\limits_{x \to 0^+} \frac{x}{p}\left\{\frac{q}{x}\right\} = \frac{q}{p} - 0\times\left(finite\right) \left(0 \le \left\{\frac{q}{x}\right\} < 1\right) = \frac{q}{p}$