List questions from uniform-continuity

Published on 25 Mar 2026 - 16:12

305

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Conditions for $f(x_n,y_n) - f(x_0, y_n) \to 0$ if $(x_n,y_n) \to (x_0,y_0)$?

Published on 17 Jul 2018 - 1:50

53

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Extension of Uniformly Differentiable function - from open ball to $\mathbb{R}^n$

Published on 18 Jul 2018 - 21:10

79

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Prove that $\lim_{n\to \infty} x_n = 0$ if $\lvert f(x) - f(y) \rvert \leq \frac{1}{2} \lvert x - y \rvert$ , $f(0) = 0$ and $x_n = f(x_{n-1})$

Published on 22 Jul 2018 - 2:35

230

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Is $f(x,y)=\frac{y}{x^2 +1}$ uniformly continuous?

Published on 27 Jul 2018 - 17:58

351

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Quotient of uniformly continuous bounded functions is uniformly continuous

Published on 29 Jul 2018 - 23:07

1k

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Uniform continuity of $\cos(x^2)$

Published on 30 Jul 2018 - 18:40

14.2k

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Show that 1/x is NOT uniformly continuous

Published on 25 Mar 2026 - 16:09

696

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Convergence of uniformly continous functions to a uniformly continous function

Published on 04 Aug 2018 - 15:26

114

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$f$ is uniformly continuity

Published on 06 Aug 2018 - 15:22

757

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Prove that $f$ is uniformly continuous on $R^n$

Published on 09 Aug 2018 - 21:02

30

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Two variable differentiable function

Published on 18 Aug 2018 - 21:05

1.4k

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Prove that f(x) = √x is uniformly continuous on [0,∞).

Published on 20 Aug 2018 - 11:18

209

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Uniform Continuity on unbounded interval

Published on 24 Aug 2018 - 7:21

490

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Prob. 14, Sec. 5.4, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: Every continuous periodic function is bounded and uniformly continuous

Published on 25 Mar 2026 - 23:08

List Question

Proving $f(x)=\sqrt{x}$ is uniformly continuous.

Conditions for $f(x_n,y_n) - f(x_0, y_n) \to 0$ if $(x_n,y_n) \to (x_0,y_0)$?

Extension of Uniformly Differentiable function - from open ball to $\mathbb{R}^n$

Prove that $\lim_{n\to \infty} x_n = 0$ if $\lvert f(x) - f(y) \rvert \leq \frac{1}{2} \lvert x - y \rvert$ , $f(0) = 0$ and $x_n = f(x_{n-1})$

Is $f(x,y)=\frac{y}{x^2 +1}$ uniformly continuous?

Quotient of uniformly continuous bounded functions is uniformly continuous

Uniform continuity of $\cos(x^2)$

Show that 1/x is NOT uniformly continuous

Convergence of uniformly continous functions to a uniformly continous function

$f$ is uniformly continuity

Prove that $f$ is uniformly continuous on $R^n$

Two variable differentiable function

Prove that f(x) = √x is uniformly continuous on [0,∞).

Uniform Continuity on unbounded interval

Prob. 14, Sec. 5.4, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: Every continuous periodic function is bounded and uniformly continuous

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