Question

Prove $ \sum\nolimits_{n=1}^{ \infty } u_n(x)$ converges uniformly at $[0,1]$, when $u_n(x) = (-1)^n(1-x)x^n$

score 18 · Answer 1 · 2026-04-14 17:25:35

18

Views

Prove $ \sum\nolimits_{n=1}^{ \infty } u_n(x)$ converges uniformly at $[0,1]$, when $u_n(x) = (-1)^n(1-x)x^n$

Published on 14 Apr 2026 - 17:25

score 329 · Answer 2 · 2026-04-13 21:30:19

329

Views

Bound on difference of derivatives of convex functions

Published on 13 Apr 2026 - 21:30

score 279 · Answer 3 · 2026-04-16 19:21:07

279

Views

Uniform convergence of real part of sequence of holomorphic functions implies uniform convergence of {$f_n$}

Published on 16 Apr 2026 - 19:21

score 26 · Answer 4 · 2026-04-14 00:32:13

26

Views

Uniform convergence of functions and sets of zeros.

Published on 14 Apr 2026 - 0:32

score 87 · Answer 5 · 2026-04-13 02:29:17

87

Views

Can we show differentiability uniformly wrt a parameter here?

Published on 13 Apr 2026 - 2:29

score 205 · Answer 6 · 2026-04-16 14:04:31

205

Views

Approximate every monotonic increasing function $f$ uniformly by a sequence $(f_n)_n$ of step functions, s.t. $f_{n+1}-f_n$ is monotonous increasing?

Published on 16 Apr 2026 - 14:04

score 75 · Answer 7 · 2026-04-16 01:24:09

75

Views

Uniform convergence of $f(x) = \sum_{n=1}^\infty \frac{(-1)^{n-1}x}{1+n^4x^2}$ on $\Bbb R$

Published on 16 Apr 2026 - 1:24

score 128 · Answer 8 · 2026-04-11 22:25:03

128

Views

Prove that this limit converges uniformly on compact subsets of Open Unit Disc

Published on 11 Apr 2026 - 22:25

score 70 · Answer 9 · 2026-04-08 17:02:08

70

Views

Approximation of functions

Published on 08 Apr 2026 - 17:02

score 49 · Answer 10 · 2026-04-13 19:50:38

49

Views

Does a finite $\sup\text{-norm}$ of a function $f_n$ on a domain $S$ imply that the series whose generic term is $f_n$ is uniformly convergent on $S$?

Published on 13 Apr 2026 - 19:50

score 217 · Answer 11 · 2026-04-13 02:15:09

217

Views

Exercise 25, Chapter 24 of Spivak's Calculus 3rd Edition

Published on 13 Apr 2026 - 2:15

score 186 · Answer 12 · 2026-04-16 04:14:04

186

Views

"Normal convergence implies uniform convergence and absolute convergence". Attempt to prove it via Weierstrass M-test. What is missing?

Published on 16 Apr 2026 - 4:14

score 836 · Answer 13 · 2026-04-16 11:35:06

836

Views

Show that the set of differentiable functions is a complete metric space, where $d(f,g)=\max_{x\in[0,1]}\{|f(x)-g(x)|+|f'(x)-g'(x)|\}$

Published on 16 Apr 2026 - 11:35

score 35 · Answer 14 · 2026-04-15 16:17:39

35

Views

A sequence of functions each having a zero and converging uniformly to a non-vanishing function.

Published on 15 Apr 2026 - 16:17

score 64 · Answer 15 · 2026-04-17 11:50:12

64

Views

Convergence of the series $ \frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\frac{8x^7}{1+x^8}+...$

Published on 17 Apr 2026 - 11:50

List Question

Prove $ \sum\nolimits_{n=1}^{ \infty } u_n(x)$ converges uniformly at $[0,1]$, when $u_n(x) = (-1)^n(1-x)x^n$

Bound on difference of derivatives of convex functions

Uniform convergence of real part of sequence of holomorphic functions implies uniform convergence of {$f_n$}

Uniform convergence of functions and sets of zeros.

Can we show differentiability uniformly wrt a parameter here?

Approximate every monotonic increasing function $f$ uniformly by a sequence $(f_n)_n$ of step functions, s.t. $f_{n+1}-f_n$ is monotonous increasing?

Uniform convergence of $f(x) = \sum_{n=1}^\infty \frac{(-1)^{n-1}x}{1+n^4x^2}$ on $\Bbb R$

Prove that this limit converges uniformly on compact subsets of Open Unit Disc

Approximation of functions

Does a finite $\sup\text{-norm}$ of a function $f_n$ on a domain $S$ imply that the series whose generic term is $f_n$ is uniformly convergent on $S$?

Exercise 25, Chapter 24 of Spivak's Calculus 3rd Edition

"Normal convergence implies uniform convergence and absolute convergence". Attempt to prove it via Weierstrass M-test. What is missing?

Show that the set of differentiable functions is a complete metric space, where $d(f,g)=\max_{x\in[0,1]}\{|f(x)-g(x)|+|f'(x)-g'(x)|\}$

A sequence of functions each having a zero and converging uniformly to a non-vanishing function.

Convergence of the series $ \frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\frac{8x^7}{1+x^8}+...$

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