Real Analysis | The uniform continuity of sqrt(x).

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We show that the square root function is uniformly continuous on its domain.

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Love your videos. I wish the YT Algorithm had introduced you earlier.

kinpatu

In fact |√x-√y|≤√|x-y| for all non-negative x and y. So it's uniformly continuous.

pierineri

Your videos helps me a lot to read U.A by Stephen Abott, thanks you so much

ranitacab

Thanks for doing all kinds of tutorials! Even ones that might be not as popular!
Very appreciated 🙏❤️

neur

at 6:22 in your scratch work, aren't you proving that sqrt(x) is a Lipschitz function?
and all Lipschitz functions are uniformly continuos

juanfa

On the open set of ordinal integers between zeroth and second.

jimskea

Great problem sir, waiting for more of your physics videos.

yazhineet.s

You could have also picked δ = min{δ_1, δ_2, 1} and that still confines x and y to one of [0, 2] or [1, inf).

charlottedarroch

This is the information I was looking for, I had many doubts, thank you very much my friend.✨👍

SalomonChing

But sir what if we choose x in 0, 1 and y in 1, +infinity how would your result hold in this case

tryhxrd.

Is step function is uniformly continuous

uniqueideas

Creo que Mr.Penn debe ser más ordenado y escribir un poco más grandes las letras.

leonardoavila

Sir I'm an 8th grader and having problems while factoring cubics and quartics, could you kindly help me

chessematics

All of this complicated equations and dividing into those two cases is unnecessary.
Just use delta = epsilon^2 and you're basically immediately done.

backyard

Consider going directly to absolute continuity, so a function can be recovered by integrating its derivative. Key for calculus.

get

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