hello..following the PNT we know that(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{\psi(x)}{x}\rightarrow 1 [/tex] and

[tex] \frac{\pi(x)}{Li(x)}\rightarrow 1 [/tex]

my question is "how fast" do the expressions:

[tex] |\frac{\psi(x)}{x}-1|=|f(x)| [/tex] and

[tex] |\frac{\pi(x)}{Li(x)}-1|=|g(x)| [/tex] tend to 0 ?

in the sense that for example will the expressions...

[tex] f(x)x^{1/2} [/tex] and [tex] g(x)x^{1/2} [/tex] tend to 0 or will they tend to infinite?... (to give a clearer explanation)

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# How fast?

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