(adsbygoogle = window.adsbygoogle || []).push({}); Does this improper integral converge???

I have an interesting problem that has been bothering me.

Given:

f(x)=1/x

g(x)= (any continuous, non-negative function)

g(x)<f(x)

A = (a positive constant)

I want to know:

Does the integral of g(x) from A to +infinity converge? Or is it impossible to determine?

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# Does this improper integral converge?

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