It depends on where f(x) ~ g(x)
And what does f(x) ~ g(x) mean ? It means that there exists such as , where tends to be very small as approaching the domain where f(x) ~ g(x).
This doesn't impeach f(x) to be inferior to g(x)...
but what relating to the classic ....I am pretty sure that ...but assuming the limit exists that then ...I am not sure that is the best example but Its the only one I can think of right now...so would you still agree with the original inequality?