Question

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

score 177 · Answer 1 · 2026-04-14 10:25:10

177

Views

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Published on 14 Apr 2026 - 10:25

score 112 · Answer 2 · 2026-04-16 03:12:35

112

Views

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Published on 16 Apr 2026 - 3:12

score 43 · Answer 3 · 2026-04-13 09:41:54

43

Views

Uniform convergence of logarithm on a compact set.

Published on 13 Apr 2026 - 9:41

score 41 · Answer 4 · 2026-04-15 11:17:20

41

Views

If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

Published on 15 Apr 2026 - 11:17

score 303 · Answer 5 · 2026-04-13 10:28:21

303

Views

Infinite sum smoothness Proof

Published on 13 Apr 2026 - 10:28

score 19 · Answer 6 · 2026-04-13 03:38:49

19

Views

Convergence of two binomials with equal n as their parameters converge

Published on 13 Apr 2026 - 3:38

score 136 · Answer 7 · 2026-04-16 12:09:53

136

Views

Find region of convergence of double power series

Published on 16 Apr 2026 - 12:09

score 87 · Answer 8 · 2026-04-15 03:01:39

87

Views

Does the series $s_n(x)=\sum^{n}_{k=0}\frac{e^{-kx}}{1+kx}$ converge uniformly over $ [1,2]?$

Published on 15 Apr 2026 - 3:01

score 1.8k · Answer 9 · 2026-04-16 21:36:31

1.8k

Views

If $\{f_n\}$ converges uniformly on $(a,b)$, $\{f_{n}(a)\}$ and $\{f_{n}(b)\}$ converge pointwise, then it converges uniformly on $[a,b]$

Published on 16 Apr 2026 - 21:36

score 575 · Answer 10 · 2026-04-15 18:07:34

575

Views

Uniform Convergence of $\sum_{n=1}^{\infty} \frac{\sin(nx)}{\sqrt{n}}, [0, 2\pi]$ by using Cauchy's test or Weierstrass-M test

Published on 15 Apr 2026 - 18:07

score 604 · Answer 11 · 2026-04-14 19:22:02

604

Views

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Published on 14 Apr 2026 - 19:22

score 65 · Answer 12 · 2026-04-13 07:09:28

65

Views

Using definition to show that $x^n$ on [0,1] is not uniform convergent

Published on 13 Apr 2026 - 7:09

score 201 · Answer 13 · 2026-04-09 11:44:51

201

Views

Prove that $f_n(x)=\sin{\sqrt{x+4n^2\pi ^2}}\,,\;x\geq 0$ is equicontinous on $[0,+\infty)$

Published on 09 Apr 2026 - 11:44

score 319 · Answer 14 · 2026-04-12 16:12:03

319

Views

relaxation on Dini's Theorem

Published on 12 Apr 2026 - 16:12

score 2.8k · Answer 15 · 2026-04-09 15:23:44

2.8k

Views

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

Published on 09 Apr 2026 - 15:23

List Question

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Uniform convergence of logarithm on a compact set.

If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

Infinite sum smoothness Proof

Convergence of two binomials with equal n as their parameters converge

Find region of convergence of double power series

Does the series $s_n(x)=\sum^{n}_{k=0}\frac{e^{-kx}}{1+kx}$ converge uniformly over $ [1,2]?$

If $\{f_n\}$ converges uniformly on $(a,b)$, $\{f_{n}(a)\}$ and $\{f_{n}(b)\}$ converge pointwise, then it converges uniformly on $[a,b]$

Uniform Convergence of $\sum_{n=1}^{\infty} \frac{\sin(nx)}{\sqrt{n}}, [0, 2\pi]$ by using Cauchy's test or Weierstrass-M test

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Using definition to show that $x^n$ on [0,1] is not uniform convergent

Prove that $f_n(x)=\sin{\sqrt{x+4n^2\pi ^2}}\,,\;x\geq 0$ is equicontinous on $[0,+\infty)$

relaxation on Dini's Theorem

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

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