Question

Uniform convergence of $f_n (x)=x^{2} - \frac{x}{n}$ on $[0, 1]$.

score 42 · Answer 1 · 2026-04-17 10:40:01

42

Views

Uniform convergence of $f_n (x)=x^{2} - \frac{x}{n}$ on $[0, 1]$.

Published on 17 Apr 2026 - 10:40

score 84 · Answer 2 · 2026-04-16 00:47:09

84

Views

Proving discontinuity at $x=0$ for $f(x)=\sum_{n=0}^{\infty} \sin^{2}(nx)/ (1+n^{2} x^{2})$

Published on 16 Apr 2026 - 0:47

score 154 · Answer 3 · 2026-04-17 22:34:17

154

Views

Uniform Convergence of $f_n^k$ and polynomial

Published on 17 Apr 2026 - 22:34

score 50 · Answer 4 · 2026-04-16 10:42:25

50

Views

Proof of uniform convergence of $f_n(x) = \dfrac{x^n}{1+x^n}$ on every interval $[b, \infty[$ with $b>1$

Published on 16 Apr 2026 - 10:42

score 699 · Answer 5 · 2026-04-17 06:44:29

699

Views

Why $f_n(x)=\sqrt[n]{x}$ on $[0,1]$ doesn't converge uniformly?

Published on 17 Apr 2026 - 6:44

score 460 · Answer 6 · 2026-04-16 20:12:41

460

Views

Uniform and pointwise convergence of $ f_n(x)= \begin{cases} 0,\ x\leq n \\ x-n, \ x\geq n \end{cases} $ and $f_n(x)=x^n-x^{2n}$

Published on 16 Apr 2026 - 20:12

score 69 · Answer 7 · 2026-04-15 11:51:01

69

Views

Uniform convergence of series of functions given convergence of coefficients

Published on 15 Apr 2026 - 11:51

score 2.6k · Answer 8 · 2026-04-15 00:29:43

2.6k

Views

Show that $\sum_{n=1}^\infty \ \frac{x}{n(1+nx^2)}$ converges uniformly on $R$.

Published on 15 Apr 2026 - 0:29

score 258 · Answer 9 · 2026-04-16 02:46:48

258

Views

Uniform convergence of $\sum\limits_{n=1}^{+\infty} \left(\sin{{1} \over {n}}\right) x^n$

Published on 16 Apr 2026 - 2:46

score 279 · Answer 10 · 2026-04-17 03:52:03

279

Views

Reciprocal of the Weierstrass $M$ test.

Published on 17 Apr 2026 - 3:52

score 94 · Answer 11 · 2026-04-11 11:51:30

94

Views

Pointwise and uniform convergence of $\sum\limits_{n=1}^{+\infty}(-1)^n\frac{x}{x+e^{-nx}}$ $\quad$ $x\in R$

Published on 11 Apr 2026 - 11:51

score 89 · Answer 12 · 2026-04-16 00:41:40

89

Views

Uniform convergence of the series of functions $\sum\limits_{n=1}^{+\infty} {n^n} {\arctan({x}^{n^3})}$

Published on 16 Apr 2026 - 0:41

score 52 · Answer 13 · 2026-04-09 17:13:54

52

Views

Proof Verification for Uniform Convergence on Sequence of Functions

Published on 09 Apr 2026 - 17:13

score 136 · Answer 14 · 2026-04-15 01:06:46

136

Views

Non-uniform convergence of improper integrals II

Published on 15 Apr 2026 - 1:06

score 26 · Answer 15 · 2026-04-16 22:51:38

26

Views

Semi-locally uniform convergence

Published on 16 Apr 2026 - 22:51

List Question

Uniform convergence of $f_n (x)=x^{2} - \frac{x}{n}$ on $[0, 1]$.

Proving discontinuity at $x=0$ for $f(x)=\sum_{n=0}^{\infty} \sin^{2}(nx)/ (1+n^{2} x^{2})$

Uniform Convergence of $f_n^k$ and polynomial

Proof of uniform convergence of $f_n(x) = \dfrac{x^n}{1+x^n}$ on every interval $[b, \infty[$ with $b>1$

Why $f_n(x)=\sqrt[n]{x}$ on $[0,1]$ doesn't converge uniformly?

Uniform and pointwise convergence of $ f_n(x)= \begin{cases} 0,\ x\leq n \\ x-n, \ x\geq n \end{cases} $ and $f_n(x)=x^n-x^{2n}$

Uniform convergence of series of functions given convergence of coefficients

Show that $\sum_{n=1}^\infty \ \frac{x}{n(1+nx^2)}$ converges uniformly on $R$.

Uniform convergence of $\sum\limits_{n=1}^{+\infty} \left(\sin{{1} \over {n}}\right) x^n$

Reciprocal of the Weierstrass $M$ test.

Pointwise and uniform convergence of $\sum\limits_{n=1}^{+\infty}(-1)^n\frac{x}{x+e^{-nx}}$ $\quad$ $x\in R$

Uniform convergence of the series of functions $\sum\limits_{n=1}^{+\infty} {n^n} {\arctan({x}^{n^3})}$

Proof Verification for Uniform Convergence on Sequence of Functions

Non-uniform convergence of improper integrals II

Semi-locally uniform convergence

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