siriusmart@lemmy.worldM to

Daily Maths Challenges@lemmy.world · 8 months ago

[2024/05/15] Differentiability implies continuity

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11

[2024/05/15] Differentiability implies continuity

siriusmart@lemmy.worldM to

Daily Maths Challenges@lemmy.world · 8 months ago

6

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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siriusmart@lemmy.worldOPM
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8 months ago
Hint:

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

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