Suppose
lim_{x -> infty} { log f(x) / log x } = c ,
where c is a constant.
Can we prove that:
f(x) = b x^c + lower order terms,
where b is something independent of x ?
can anyone show me how to prove this? or maybe it is incorrect?
tks
This really is what i want to prove.
It looks must-be-true, but i did get stuck when i tried to write down a rigorous proof,
since i didn't know the small oh notation is available here and i was worried about the
fact that log x does not exist for x->infty, so...
Your answer helped me a lot. tks again