Question

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

score 39 · Answer 1 · 2019-02-08 14:15:03

39

Views

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

Published on 08 Feb 2019 - 14:15

score 81 · Answer 2 · 2019-02-08 14:47:47

81

Views

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

Published on 08 Feb 2019 - 14:47

score 151 · Answer 3 · 2019-02-08 15:51:22

151

Views

Uniform Convergence of $f_n^k$ and polynomial

Published on 08 Feb 2019 - 15:51

score 47 · Answer 4 · 2019-02-08 19:30:18

47

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 08 Feb 2019 - 19:30

score 696 · Answer 5 · 2019-02-09 23:31:42

696

Views

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

Published on 09 Feb 2019 - 23:31

score 457 · Answer 6 · 2019-02-11 00:51:11

457

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 11 Feb 2019 - 0:51

score 66 · Answer 7 · 2019-02-11 03:51:42

66

Views

Uniform convergence of series of functions given convergence of coefficients

Published on 11 Feb 2019 - 3:51

score 2.6k · Answer 8 · 2019-02-11 05:47:01

2.6k

Views

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

Published on 11 Feb 2019 - 5:47

score 255 · Answer 9 · 2019-02-12 17:41:57

255

Views

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

Published on 12 Feb 2019 - 17:41

score 274 · Answer 10 · 2019-02-12 22:17:36

274

Views

Reciprocal of the Weierstrass $M$ test.

Published on 12 Feb 2019 - 22:17

score 93 · Answer 11 · 2026-03-23 14:07:10

93

Views

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

Published on 23 Mar 2026 - 14:07

score 86 · Answer 12 · 2019-02-14 11:52:33

86

Views

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

Published on 14 Feb 2019 - 11:52

score 51 · Answer 13 · 2026-03-22 23:32:19

51

Views

Proof Verification for Uniform Convergence on Sequence of Functions

Published on 22 Mar 2026 - 23:32

score 133 · Answer 14 · 2019-02-14 22:27:39

133

Views

Non-uniform convergence of improper integrals II

Published on 14 Feb 2019 - 22:27

score 23 · Answer 15 · 2019-02-15 10:33:18

23

Views

Semi-locally uniform convergence

Published on 15 Feb 2019 - 10:33

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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