If we know: $$f_1, f_2, g_1, g_2, c_1, c_2 > 0$$ $$f_1( n ) \leq c_1 g_1( n ) ~\forall n \geq n_1$$ $$f_2(n) \leq c_2 g_2( n ) ~\forall n \geq n_2$$ Then: $$f_1(n)f_2(n) \leq c_1c_2g_1(n)g_2(n)$$ but for what n? An example that I did yielded $n = \sqrt{n_1n_2}$ but I cannot prove why this is or if it is general.
2026-03-30 08:32:55.1774859575
Asymptotic analysis of a product of functions
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