@siriusmartM to Daily Maths Challenges • 29 days ago[2024/05/15] Differentiability implies continuityimagemessage-square6arrow-up19arrow-down10file-text
arrow-up19arrow-down1image[2024/05/15] Differentiability implies continuity@siriusmartM to Daily Maths Challenges • 29 days agomessage-square6file-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-square@siriusmartOPMlink3•edit-229 days agoHint: spoiler Try show that for the statement to be true, the derivative has to be defined. There are 2 definitions for the derivative, either would be useful in the proof Solution spoiler https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd solutions/2024-05-15_differentiablility-implies-continuity.html
Hint:
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Solution
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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd solutions/2024-05-15_differentiablility-implies-continuity.html![](https://lemmy.world/pictrs/image/e297427c-59ad-46d9-99e8-bad9a90203c7.png)