Talk:L'Hôpital's Rule/Corollary 2

Doesn't the fact that $f$ and $g$ are continuous on $\closedint a b$ contradict the fact that they diverge at $a$? I think the statement here might be flawed. --CircuitCraft (talk) 02:54, 25 September 2023 (UTC)
 * Abramowitz and Stegun (the only source for this specific version of this result I have found) just defines differentiability on $\openint a b$. I can't see why continuity on that interval was specified for the main result, even, but Binmore (cited in Proof 2) specifies it, as it's specified for the Cauchy mean value theorem (which he uses to prove it). I would have thought that differentiability on $\openint a b$ should be enough for anybody. Requiring continuity at the endpoints seems to be overegging it. --prime mover (talk) 05:08, 25 September 2023 (UTC)