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bio website ondrejcertik.com
location Los Alamos, NM
age 30
visits member for 2 years, 3 months
seen Jul 28 at 4:07

Jul
2
awarded  Curious
Nov
20
accepted Derivative of big O symbol
Nov
18
revised Derivative of big O symbol
Clarify the x=0 point once more, just to be absolutely clear we are not dealing with x=oo
Nov
18
comment Derivative of big O symbol
$\sin(x^2)$ is infinitely differentiable at $x=0$ and the series is just a polynomial, so for it $O'(1) = O(1)$. You might be expanding around $x=\infty$, while I am asking about $x=0$. I clarified the question about this.
Nov
18
revised Derivative of big O symbol
Clarify that we only deal with x=0 case
Nov
18
asked Derivative of big O symbol
May
9
awarded  Yearling
Feb
25
awarded  Nice Question
Jan
16
awarded  Commentator
Jan
16
comment Is odd continuous function differentiable at $x=0$?
@N.S. Please do, I didn't want to put your solution into answers myself.
Jan
16
comment Solution of functional equation $f(x/f(x)) = 1/f(x)$?
Very nice! So if the function $f(x)$ is analytic, then you prove that $f(x)=1$. Assuming only that $f(x)$ is continuous, then the only possible other solutions are not analytic. That helps a lot.
Jan
16
comment Solution of functional equation $f(x/f(x)) = 1/f(x)$?
Right. So the domain of $g(x)$ must be an interval (e.g. not a union of two disjoint intervals). However, what if we only solve this on an interval [1, 10], let's say? I guess we would run into some contradictions with domains and ranges in the functional equation.
Jan
16
comment Solution of functional equation $f(x/f(x)) = 1/f(x)$?
Because $g(x)=1/x$ is also a solution of $g(g(x))$ and somehow it got eliminated. So something is not right. (Of course, it would get eliminated later anyway due to $g'(0)=1$, but that's not the point.)
Jan
16
revised Solution of functional equation $f(x/f(x)) = 1/f(x)$?
added 969 characters in body
Jan
16
awarded  Editor
Jan
16
revised Solution of functional equation $f(x/f(x)) = 1/f(x)$?
Grammar.
Jan
16
asked Solution of functional equation $f(x/f(x)) = 1/f(x)$?
Jan
16
comment Is odd continuous function differentiable at $x=0$?
N.S., you are right! $\frac{f(x)}{x} = \sin\frac{1}{x^2}$ which oscillates between -1 and 1 and so the limit does not exist. So this function is not differentiable at $x=0$. Thanks!
Jan
16
asked Is odd continuous function differentiable at $x=0$?
Oct
25
awarded  Tumbleweed