Question

How do you prove that $\frac{\sin x}{n \sin (\frac{x}{n})}$ converges uniformly?

score 109 · Answer 1 · 2026-04-16 17:11:08

109

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How do you prove that $\frac{\sin x}{n \sin (\frac{x}{n})}$ converges uniformly?

Published on 16 Apr 2026 - 17:11

score 67 · Answer 2 · 2026-04-13 05:53:26

67

Views

Does the Hölder coefficient tend to zero?

Published on 13 Apr 2026 - 5:53

score 207 · Answer 3 · 2026-04-12 08:54:43

207

Views

Topology of local uniform convergence

Published on 12 Apr 2026 - 8:54

score 183 · Answer 4 · 2026-04-11 16:00:11

183

Views

Uniform convergence to swap summation and integration

Published on 11 Apr 2026 - 16:00

score 106 · Answer 5 · 2026-04-10 22:21:56

106

Views

Norm turning $C^\infty(\overline{B(0,1)})$ into a Banach space?

Published on 10 Apr 2026 - 22:21

score 217 · Answer 6 · 2026-04-14 14:07:25

217

Views

Show that the product of bounded functions converges uniformly

Published on 14 Apr 2026 - 14:07

score 83 · Answer 7 · 2026-04-15 13:04:32

83

Views

Why do I need uniform convergence?

Published on 15 Apr 2026 - 13:04

score 176 · Answer 8 · 2026-04-15 18:07:20

176

Views

Uniform convergence of $f_n(x)=\frac1{1+nx}$ on $(0,\infty)$

Published on 15 Apr 2026 - 18:07

score 385 · Answer 9 · 2026-04-16 08:54:00

385

Views

Let $f_n(x)=\frac{1}{nx+1}$ and $g_n(x)=\frac{x}{nx+1}$ for $x\in (0,1)$. Show that $f_n$ doesn't converge uniformly but that $g_n$ does

Published on 16 Apr 2026 - 8:54

score 49 · Answer 10 · 2026-04-17 01:20:44

49

Views

Does $\lim_{a\to 0}\int_1^\infty f\left(\sqrt{a^2+x^2}\right)dx=\int_1^\infty f\left(x\right)dx$ for smooth, rapidly decaying $f$?

Published on 17 Apr 2026 - 1:20

score 34 · Answer 11 · 2026-04-16 19:32:28

34

Views

If $f_n\to f$ uniformly, then $\min_{[a,b]}f_n \to \min_{[a,b]}f$

Published on 16 Apr 2026 - 19:32

score 492 · Answer 12 · 2026-04-16 22:28:09

492

Views

Let $f_n$ sequence of continuous functions on $[a,b]$, $\lim_{n\to \infty}f_n(x)=f(x)$ uniformly on $(a,b)$. Show $f_n\mapsto f$ uniformly on $[a,b]$

Published on 16 Apr 2026 - 22:28

score 39 · Answer 13 · 2026-04-09 16:58:06

39

Views

Uniform convergence over composition functions

Published on 09 Apr 2026 - 16:58

score 120 · Answer 14 · 2026-04-15 05:09:03

120

Views

Showing that $n\sin(x/n)$ does not converge uniformly on $\mathbb{R}$

Published on 15 Apr 2026 - 5:09

score 223 · Answer 15 · 2026-04-16 18:10:56

223

Views

Taylor series of $\ln(x)$ not uniformly convergent

Published on 16 Apr 2026 - 18:10

List Question

How do you prove that $\frac{\sin x}{n \sin (\frac{x}{n})}$ converges uniformly?

Does the Hölder coefficient tend to zero?

Topology of local uniform convergence

Uniform convergence to swap summation and integration

Norm turning $C^\infty(\overline{B(0,1)})$ into a Banach space?

Show that the product of bounded functions converges uniformly

Why do I need uniform convergence?

Uniform convergence of $f_n(x)=\frac1{1+nx}$ on $(0,\infty)$

Let $f_n(x)=\frac{1}{nx+1}$ and $g_n(x)=\frac{x}{nx+1}$ for $x\in (0,1)$. Show that $f_n$ doesn't converge uniformly but that $g_n$ does

Does $\lim_{a\to 0}\int_1^\infty f\left(\sqrt{a^2+x^2}\right)dx=\int_1^\infty f\left(x\right)dx$ for smooth, rapidly decaying $f$?

If $f_n\to f$ uniformly, then $\min_{[a,b]}f_n \to \min_{[a,b]}f$

Let $f_n$ sequence of continuous functions on $[a,b]$, $\lim_{n\to \infty}f_n(x)=f(x)$ uniformly on $(a,b)$. Show $f_n\mapsto f$ uniformly on $[a,b]$

Uniform convergence over composition functions

Showing that $n\sin(x/n)$ does not converge uniformly on $\mathbb{R}$

Taylor series of $\ln(x)$ not uniformly convergent

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