Question

Given $f:[0,8]\to \mathbb{R}$ be defined by $f(x)=x^{(1/3)}$

score 67 · Answer 1 · 2026-03-20 11:56:23

67

Views

Given $f:[0,8]\to \mathbb{R}$ be defined by $f(x)=x^{(1/3)}$

Published on 20 Mar 2026 - 11:56

score 482 · Answer 2 · 2026-03-19 18:34:01

482

Views

Show that the function $f: x \rightarrow x^2$ is uniformly continuous on the set $S = \bigcup \{[n,n + n^{-2}] ~|~n \in \mathbb N\}$

Published on 19 Mar 2026 - 18:34

score 604 · Answer 3 · 2026-03-20 10:48:27

604

Views

Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

Published on 20 Mar 2026 - 10:48

score 911 · Answer 4 · 2026-03-20 10:04:42

911

Views

A sequence of continuous functions that converges uniformly to a continuous function is equicontinuous

Published on 20 Mar 2026 - 10:04

score 109 · Answer 5 · 2026-03-24 21:44:28

109

Views

Why can't all pointwise continuous functions preserve Cauchy sequences?

Published on 24 Mar 2026 - 21:44

score 866 · Answer 6 · 2026-03-19 19:53:06

866

Views

Uniformly continuous in $(a,b)$ if and only if uniformly continuous in $[a,b]$?

Published on 19 Mar 2026 - 19:53

score 468 · Answer 7 · 2026-03-20 09:23:16

468

Views

Can the composition of two non-uniformly continuous functions be uniformly continuous?

Published on 20 Mar 2026 - 9:23

score 125 · Answer 8 · 2026-03-20 11:16:55

125

Views

Prove that $\lim_{n \to \infty} \frac{1}{2^n}\sum_{k=0}^n(-1)^k {n\choose k}f\left(\frac{k}{n} \right)=0$

Published on 20 Mar 2026 - 11:16

score 152 · Answer 9 · 2026-03-20 04:35:01

152

Views

How to check uniform continuity on disconnected set

Published on 20 Mar 2026 - 4:35

score 77 · Answer 10 · 2026-03-20 04:18:49

77

Views

Proving that $f(x)$ isn't uniformly continuous...

Published on 20 Mar 2026 - 4:18

score 29 · Answer 11 · 2026-03-20 09:53:35

29

Views

Is this a sufficient condition for non uniform continuity?

Published on 20 Mar 2026 - 9:53

score 870 · Answer 12 · 2026-03-24 19:52:33

870

Views

Density of Lipschitz functions in the set of uniformly continuous functions

Published on 24 Mar 2026 - 19:52

score 146 · Answer 13 · 2026-03-21 20:25:32

Let $f:[0,1] \to [0,1]$ be a continuous function with fixed points $0, 1$. Prove that if $f \circ f \circ f...$ converges uniformly, then $f(x) = x$.

score 70 · Answer 14 · 2026-03-25 01:29:09

70

Views

Prove that $f(x,y):[0,1]^2 \to \mathbb R$ a continuous function can be approximated by a finite sum of $g_k(x)h_k(y)$

Published on 25 Mar 2026 - 1:29

score 1.1k · Answer 15 · 2026-03-22 10:27:32

1.1k

Views

Uniform continuity of $\frac{1}{x^4+1}$ using mean value theorem

Published on 22 Mar 2026 - 10:27

List Question

Given $f:[0,8]\to \mathbb{R}$ be defined by $f(x)=x^{(1/3)}$

Show that the function $f: x \rightarrow x^2$ is uniformly continuous on the set $S = \bigcup \{[n,n + n^{-2}] ~|~n \in \mathbb N\}$

Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

A sequence of continuous functions that converges uniformly to a continuous function is equicontinuous

Why can't all pointwise continuous functions preserve Cauchy sequences?

Uniformly continuous in $(a,b)$ if and only if uniformly continuous in $[a,b]$?

Can the composition of two non-uniformly continuous functions be uniformly continuous?

Prove that $\lim_{n \to \infty} \frac{1}{2^n}\sum_{k=0}^n(-1)^k {n\choose k}f\left(\frac{k}{n} \right)=0$

How to check uniform continuity on disconnected set

Proving that $f(x)$ isn't uniformly continuous...

Is this a sufficient condition for non uniform continuity?

Density of Lipschitz functions in the set of uniformly continuous functions

Let $f:[0,1] \to [0,1]$ be a continuous function with fixed points $0, 1$. Prove that if $f \circ f \circ f...$ converges uniformly, then $f(x) = x$.

Prove that $f(x,y):[0,1]^2 \to \mathbb R$ a continuous function can be approximated by a finite sum of $g_k(x)h_k(y)$

Uniform continuity of $\frac{1}{x^4+1}$ using mean value theorem

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