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Asymptotic behavior of functions, asymptotic series and related topics
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Asymptotic estimates for the Exponential
This is a standard calculus question. Let $z(n) = (1−f(n))^{g(n)}$.
Then $\log z(n) = g(n) \log( 1 - f(n))$. Assuming $f(n)\rightarrow 0$, one
has $\log z(n)/( f(n)g(n) ) \rightarrow -1$. For your
p …