Why is a differentiable function necessarily continuous? - Week 3 - Lecture 7 - Mooculus

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  1. Jim Fowler
  2. mathematics
  3. calculus
  4. mooculus
  5. math
  6. maths
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Very clear, instructive and student-friendly video! I have a simple remark, more logical than mathematical. Maybe saying at the end of the video that differentiability and continuity are connected could be misleading. The reason is that " being connected to" is ( in ordinary language) a symmetric relation. So it suggests that continuity is linked to differentiability in the same way as differentiability is linked to continuity. But, as you explained before very clearly, the implication does not "work" both ways: differentiability is actually " connected" to continuity ( continuity is a necessary condition of differentiability) but continuity is not connected to differentiability ( continuity is not a sufficient condition of differentiability).

raylittlerock
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I also know examples of cloudy days without rain: if it is snow, hail, sleet, et.c. Then it isn't really rain faling.

I know a function that is continuous everywhere, but never differentiable:

sum(n=0 to infinity) (a^n * cos (pi(b^n)x))

martinnolin
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I love your energy!! Thanks your video was of great help!!

nourmahmoud