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

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- Jul 20th 2010, 07:40 AMjillfind a function from the limit
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 - Jul 20th 2010, 09:12 AMFailure
- Jul 20th 2010, 10:36 AMjill
- Jul 20th 2010, 11:37 AMFailure
- Jul 20th 2010, 11:48 AMjill
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 ;)