Talk:L'Hôpital's Rule/Also defined as

There is no requirement that $\map f x \to \infty$ as $x \to b$, so the function cannot be proven discontinuous there. In fact, we could take $b' = \dfrac {a + b} 2$, and the theorem would apply on $\hointl a {b'}$, but $f$ would necessarily be continuous at $b'$. --CircuitCraft (talk) 18:44, 25 September 2023 (UTC)


 * That's not the point. You can have it dicsontinuous at either end, or both. --prime mover (talk) 19:26, 25 September 2023 (UTC)


 * You can have discontinuities on either end, but the assertion is that $f$ and $g$ must have discontinuities on $a$ and $b$ (in Corollary 2). This is not true. They may have a discontinuity at $b$, but they must have a discontinuity at $a$. --CircuitCraft (talk) 19:29, 25 September 2023 (UTC)


 * Clarified the language. --prime mover (talk) 19:45, 25 September 2023 (UTC)