List questions from uniform-continuity

Published on 14 Apr 2026 - 13:46

308

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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 16 Apr 2026 - 7:49

56

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

Published on 14 Apr 2026 - 0:22

82

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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 17 Apr 2026 - 3:46

233

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

Published on 12 Apr 2026 - 13:24

354

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Quotient of uniformly continuous bounded functions is uniformly continuous

Published on 09 Apr 2026 - 22:49

1k

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

Published on 15 Apr 2026 - 14:22

14.2k

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Show that 1/x is NOT uniformly continuous

Published on 12 Apr 2026 - 15:20

698

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Convergence of uniformly continous functions to a uniformly continous function

Published on 13 Apr 2026 - 21:52

117

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$f$ is uniformly continuity

Published on 15 Apr 2026 - 0:27

760

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

Published on 13 Apr 2026 - 9:44

35

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Two variable differentiable function

Published on 17 Apr 2026 - 13:07

1.4k

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

Published on 12 Apr 2026 - 23:42

212

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Uniform Continuity on unbounded interval

Published on 13 Apr 2026 - 20:07

493

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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 10 May 2026 - 18:43

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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