if : f(2x)=4x-2f(x)+x² , f(0)=0 find lim x---> 0 ( 2x-f(x) / x² )?

Question

sryy i meant f(2x)=4x-2f(x)-x^2

Answer 1

Hmm. I have a tricky thought.

Let L be that limit.

Then L = lim x -->0 of 1/2 * (f(2x) - x^2)/x^2 = -1/2 + 1/2 * M, where M = lim x-->0 f(2x)/x^2 = 4 * lim y-->0 f(y)/y^2.

So if L exists than so does M. On the other hand, if you just expand L into two terms, it seems that if L exists M can NOT exist.

Unless I made an error in there somewhere, L doesn't exist, and you can tighten that up into a proof of same.