Prove that $\lim_{x\to \infty}\frac{3}{x}\lfloor\frac{x}{4}\rfloor=\frac{3}{4}$

Question

Prove that $\lim_{x\to \infty}\frac{3}{x}\lfloor\frac{x}{4}\rfloor=\frac{3}{4}$

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If i put $x\to\infty$,the $\frac{3}{x}$ tends to zero and the $\lfloor\frac{x}{4}\rfloor$ tends to $\infty$.I do not know how they multiplied to get finite $\frac{3}{4}$.

Answer 1

Hint $$\frac{x}{4}-1 \leq \left\lfloor\frac{x}{4}\right\rfloor \leq \frac{x}{4}$$

Answer 2

write [x/4]=(x/4)-{x/4} now regroup the terms.From the first limit you get the answer. Coming to the second limit {x/4} always lies in the range (0,1) so it is zero. This completes the proof.