I ask this question here, and I was told that using squezze theorem I could solve it, but using this idea in this limit I end with.
$\frac{b}{a} \leq \lim_{x\to0^+}{\frac bx\left[\frac xa\right]} \leq \infty$
Why?
2026-03-26 22:18:10.1774563490
Why $\lim_{x\to0^+}{\frac bx\left[\frac xa\right]}=0$?, where $[x] = \sup\{n \in N, n \leq x\}$
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Hint: $x-1\leq \left [ x \right ]\leq x$