this post was submitted on 15 May 2024
11 points (100.0% liked)

Daily Maths Challenges

189 readers
1 users here now

Share your cool maths problems.



Complete a challenge:


Post a challenge:


Feel free to contribute to a series by DMing the OP, or start your own challenge series.

founded 6 months ago
MODERATORS
 
  • 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)
you are viewing a single comment's thread
view the rest of the comments
[–] [email protected] 3 points 5 months ago* (last edited 5 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

spoilerhttps://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-15_differentiablility-implies-continuity.html