siriusmart@lemmy.worldM to Daily Maths Challenges@lemmy.world · 6 months ago[2024/05/15] Differentiability implies continuitylemmy.worldimagemessage-square6fedilinkarrow-up111arrow-down10file-text
arrow-up111arrow-down1image[2024/05/15] Differentiability implies continuitylemmy.worldsiriusmart@lemmy.worldM to Daily Maths Challenges@lemmy.world · 6 months agomessage-square6fedilinkfile-text
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)
minus-squarekartoffelsaftlinkfedilinkarrow-up1·6 months agoIsn’t the Weierstrass function a counterexample to the premise? Wait no, I misread. It’s the converse.
minus-squaresiriusmart@lemmy.worldOPMlinkfedilinkarrow-up1·6 months agoi thought the “default” counter example is y=|x| lol
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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