If I want to compute $$\lim_{x\to 0}\frac{f(x)+x}{x^2}$$ but only have the Taylor expansion of $f(x)$ near $0$, can I use just the first degree Taylor polynomial for computing this limit, provided the first derivative of $f(x)$ does not vanish at $0$?
@Shootforthemoon Absolutely not. You need the degree $2$ T.P. Reason: $f(x) = P_2(x) + \epsilon(x)$ where $\lim\limits_{x\to 0}\dfrac{\epsilon(x)}{x^2} = 0$.
P.S. @ShineOnYouCrazyDiamond You need to ping Ted E with TedE ... or else I get pinged too.
Hi, in [this answer](https://math.stackexchange.com/a/2696744/727383) it is claimed that the structure sheaf $\mathcal{O}_X$ is representable, in particular for $S$-schemes $\Bbb A^1_S$. However, these should only agree as set-valued sheaves right? That is to say, $\text{Hom}_S(U,\Bbb A^1)$ only has set structure, not ring structure.
I guess I could upgrade this to a group, by considering hom's to $\Bbb G_a$ (I haven't actually thought this through to make it rigorous), but I can't see how one could actually make it representable as a ring-valued sheaf.
looks like for some reason it parsed the https:// thing in your message first and posted it as a blue link without https://, at which point [this code](can't read it)
