Question

Let $f: [0,1] \to \mathbb R$ be a continuous function with $f(0)= f(1)$. Then for any $c \in [0,1/2]$ , $f(c) = f(c+1/2)$.

score 176 · Answer 1 · 2019-11-02 03:17:20

176

Views

Let $f: [0,1] \to \mathbb R$ be a continuous function with $f(0)= f(1)$. Then for any $c \in [0,1/2]$ , $f(c) = f(c+1/2)$.

Published on 02 Nov 2019 - 3:17

score 32 · Answer 2 · 2019-11-05 14:59:47

32

Views

Criterion of uniform continuity for an interval of the form $(a,\infty)$.

Published on 05 Nov 2019 - 14:59

score 65 · Answer 3 · 2019-11-09 18:27:55

65

Views

This statement is true or not?

Published on 09 Nov 2019 - 18:27

score 1.3k · Answer 4 · 2019-11-12 03:58:49

1.3k

Views

Show that $\cos x=x^3+x^2+4x$ has exactly one root in $[0,\frac{\pi}{2}]$

Published on 12 Nov 2019 - 3:58

score 264 · Answer 5 · 2019-11-13 20:18:49

264

Views

Prove constant exists such that a function is uniformly continuous

Published on 13 Nov 2019 - 20:18

score 102 · Answer 6 · 2019-11-16 06:12:57

102

Views

Is an Arbitrary Function $f$ Uniformly Continuous Over $\emptyset$

Published on 16 Nov 2019 - 6:12

score 57 · Answer 7 · 2019-11-17 03:21:57

57

Views

Disproving Uniform Continuity of a function

Published on 17 Nov 2019 - 3:21

score 251 · Answer 8 · 2019-11-17 20:01:11

251

Views

Find a function $f$ that is continuous and bounded on $[0, \infty)$ but which is not uniformly continuous on $[0, \infty)$

Published on 17 Nov 2019 - 20:01

score 27 · Answer 9 · 2019-11-19 10:41:55

27

Views

Prove $g(x) = \sum_{n=1}^{\infty} \frac{d}{dx}(-1)^n(4x)^n$ is uniformly continuous on $[-a,a]$ for each $a$ where $0 \lt a \lt \frac{1}{4}$.

Published on 19 Nov 2019 - 10:41

score 74 · Answer 10 · 2019-11-20 19:02:23

74

Views

Prove that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=0}^{n-1}|f(E_{2}^{k}(x_{n}))-f(E_{2}^{k}(x))|=0$, where ...

Published on 20 Nov 2019 - 19:02

score 117 · Answer 11 · 2019-11-21 06:47:37

117

Views

Prove that $f$ is uniformly continuous on $(a, b)$

Published on 21 Nov 2019 - 6:47

score 214 · Answer 12 · 2026-03-26 18:59:07

214

Views

Weak-Strong, Lipschitz and uniform continuity

Published on 26 Mar 2026 - 18:59

score 86 · Answer 13 · 2019-11-23 18:02:32

86

Views

Sum of uniformly continuous fuctions

Published on 23 Nov 2019 - 18:02

score 54 · Answer 14 · 2026-03-26 13:43:18

54

Views

Are these two functions $C^0$ close? (idea related to convex integration theory)

Published on 26 Mar 2026 - 13:43

score 543 · Answer 15 · 2026-03-26 18:58:25

543

Views

Uniformly Lipschitz continuously differentiable?

Published on 26 Mar 2026 - 18:58

List Question

Let $f: [0,1] \to \mathbb R$ be a continuous function with $f(0)= f(1)$. Then for any $c \in [0,1/2]$ , $f(c) = f(c+1/2)$.

Criterion of uniform continuity for an interval of the form $(a,\infty)$.

This statement is true or not?

Show that $\cos x=x^3+x^2+4x$ has exactly one root in $[0,\frac{\pi}{2}]$

Prove constant exists such that a function is uniformly continuous

Is an Arbitrary Function $f$ Uniformly Continuous Over $\emptyset$

Disproving Uniform Continuity of a function

Find a function $f$ that is continuous and bounded on $[0, \infty)$ but which is not uniformly continuous on $[0, \infty)$

Prove $g(x) = \sum_{n=1}^{\infty} \frac{d}{dx}(-1)^n(4x)^n$ is uniformly continuous on $[-a,a]$ for each $a$ where $0 \lt a \lt \frac{1}{4}$.

Prove that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=0}^{n-1}|f(E_{2}^{k}(x_{n}))-f(E_{2}^{k}(x))|=0$, where ...

Prove that $f$ is uniformly continuous on $(a, b)$

Weak-Strong, Lipschitz and uniform continuity

Sum of uniformly continuous fuctions

Are these two functions $C^0$ close? (idea related to convex integration theory)

Uniformly Lipschitz continuously differentiable?

Trending Questions

Popular # Hahtags

Popular Questions