Question

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

• A. $\frac{\left[q\right]}{p}$
• B. $0$
• C. $1$
• D. $\infty$

Answer 1

Answer: (A)

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