- Show that if a function is differentiable for an interval, it is continuous over that interval.
- A function is continuous if lim_x->a f(x) = f(a)
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Isn’t the Weierstrass function a counterexample to the premise?Wait no, I misread. It’s the converse.i thought the “default” counter example is y=|x| lol
![[2024/05/15] Differentiability implies continuity](https://lemmy.world/pictrs/image/c2d233c2-8a9e-48a7-89dd-dbe5445894fd.png){kind=link}