a neat fact about uniform continuity

Uniform Continuity and Derivatives

In this video, I present a really neat test for uniform continuity, which has to do with derivatives. Check out this video to find out what it is!

[saminzamil]

Just wanted to tell you that I love your videos. Keep it up Sir❣️

[dylank]

Continuously differentiable functions with bounded derivatives even are Lipschitz continous, as seen in your proof if we just stop at |f(x) - f(y)| <= M |x-y|

[ethandole]

I was wondering about this- good to know that it is indeed true!

[rasad]

Thankyou so much i was struggling with this topic ❤

[deeptochatterjee]

I'm guessing this is specifically for connected intervals then for the MVT to apply

[Peter_]

I don't think that it is possible to be any more charming than Dr Peyam.

[Ghjsinshshbdgdbd]

This is so neat thank you for not waiting and releasing early😫💦

[wuyqrbt]

Hello Dear Dr Peyam.
I have a request. If it's possible, please make a video (actually another one, from a to z) about Cauchy integral and Residue theorem.
Thank you

[yassinemohamed]

Mr the thoerem is not applied to the interval [a, b) .because the conditions of continous should have at the interval [a, b] but not [a, b) .else you remplace this interval by [a, oo)

[sumittete]

Hello Sir...If a function is uniformly continuous on a closed interval, could we refine the definition of uniform continuity by replacing the condition |x-y| < δ and |f(x) - f(y)| < ε with |x-y| ≤ δ implying |f(x) - f(y)| ≤ ε ?

[dwaipayansharma]

Can we use this theorem to prove that f(x) = (√x)sinx is not UC on R(since its derivative is not bounded on R)
Thanks in advance.

[e-learningtutor]

Sir can you please explain about PROBABILITY DENSITY THEORM
I was searching for this n iam not getting any proper video about it anywhere.
So, can you please help me out sir!!
Thanks sir, i like the way you lecture

[jamesshelton]

Any possibility you could do some videos on showing holder continuous functions?

[reeeeeplease]

I think the statement is even stronger, my memory might play tricks on me tho (was HW exercise):

Let f be cont. on [a, b] and diff. on (a, b). Then i) and ii) are equivalent:

i) f' is bounded
ii) f is UC on [a, b]

*As I said, I'm not sure if it's correct*


Should be intuitively correct tho; if f is UC then f can't grow "infinitely fast" (referring to def of UC), so f' should always be bounded

[Wooflays]

ASU! Hope it's working out for you!

[MathAdam]

For some reason, my profanity filter blocked the thumbnail?