Proof that f(x) = x^2 is Uniformly Continuous on (0, 1)

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Proof that f(x) = x^2 is Uniformly Continuous on (0, 1)
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Nice choice of a manageable function to illustrate the concept / definition of uniform continuity.

acdude
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i cant understand the step how dell is equal to epsilon by 2

zaidbutt
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Prove that set of rational numbers is
dense in the set of real numbers.

pradeepsao
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Hello, is it possible to prove that x^2 is continuous on R ?

Gaelrenaultdu
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Cant we just take δ=ε? Because
| 𝑥 - 𝑦 | < | 𝑥 | + | - 𝑦 | = | 𝑥 | + | 𝑦 |, since 𝑥 and 𝑦 < 1, then | 𝑥 | + | 𝑦 | implies | 𝑥 - 𝑦 | < 2 which we assume is < δ.
Then this also implies, by the same manner, that | 𝑥² - 𝑦² | < 2 < δ < ε.
So, then, couldn't δ=ε?

fellipeparreiras
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Could you please explain how did you take |x+y|<2 ?

mayurgo
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tomorrow is my exam it help me a lot ....thanks sir

Akash-lspz
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If delta=epsilon/2 then 2delta=epsilon but we want 2delta less than epsilon so I think you made a mistake there.

thelastcipher
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Is this function is uniformly continuous in whole real line??

prakashbadu
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Hi I have a question, can u answer me plz. how to proof a function 1/x^2+sinx+2 is uniformly Conti. on real numbers?

蒙娜麗莎的味道