I have function $$f(x)=\frac{1}{x^m}\prod_{i=1}^{k}(1-a_i^x)^{n_i},~~x>0$$ where $0<a_i<1, n_i\geq0$ and ${m=\sum_{i=1}^{k}n_i}.$ Is it bounded? It can be shown that $\displaystyle{lim_{x\to \infty} f(x)}=0.$ Also, $f(x)$ is a continuous function on $(0, \infty)$. If we can calculate $\lim_{x \to 0^{+} }f(x)$, we can respond to this question. Can you help me?
2026-03-28 16:20:00.1774714800
Is the following function bounded?
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