Question

The value of \(\lim _{x \rightarrow 0+} \frac{x}{p}\left[\frac{q}{x}\right]\) is
(A) \(\frac{[q]}{p}\)
(B) 0
(C) 1
(D) \(\infty\)

Answer 1

Ans: (A)
Hint \(:=\operatorname{lt}_{x \rightarrow 0^{0}} \frac{x}{p}\left(\frac{q}{x}-\left\{\frac{q}{x}\right\}\right)=\) It \(\underset{x \rightarrow 0^{0}}{\underline{p}}-\) It \(_{x \rightarrow 0^{0}} \frac{x}{p}\left\{\frac{q}{x}\right\}=\frac{q}{p}-0 \times\) (finite) \(\left(0 \leq\left\{\frac{q}{x}\right\}<1\right)=\frac{q}{p}\)