Question

What if the interval $[0,1]$ changes to $\mathbb R$ in the question?

score 58 · Answer 1 · 2019-11-05 09:03:17

58

Views

What if the interval $[0,1]$ changes to $\mathbb R$ in the question?

Published on 05 Nov 2019 - 9:03

score 409 · Answer 2 · 2019-11-06 08:39:29

409

Views

If $(f_n)$ converges uniformly to $f$, then prove that $\lim_{x\to c}\lim_{n\to \infty} f_n(x) = \lim_{n\to \infty} \lim_{x\to c}f_n(x) $

Published on 06 Nov 2019 - 8:39

score 53 · Answer 3 · 2019-11-06 09:31:30

53

Views

Is it necessarily true for $(f_n)$ to converge uniformly on $[a,b]$

Published on 06 Nov 2019 - 9:31

score 1.1k · Answer 4 · 2019-11-08 07:39:27

1.1k

Views

Show that $\{0,1\}^{[0,1]}$ is not sequentially compact

Published on 08 Nov 2019 - 7:39

score 57 · Answer 5 · 2019-11-11 19:53:13

57

Views

Calculating functional sequence

Published on 11 Nov 2019 - 19:53

score 101 · Answer 6 · 2019-11-12 15:29:59

101

Views

calculate the limit of a numerical sequence

Published on 12 Nov 2019 - 15:29

score 59 · Answer 7 · 2019-11-14 17:05:29

59

Views

Convergence of $g _ { n } ( x ) = \int _ { 0 } ^ { x }f_n(t)dt $

Published on 14 Nov 2019 - 17:05

score 69 · Answer 8 · 2019-11-14 17:07:12

69

Views

Uniform convergence of $f_n(x) = \frac{nx}{1+ n^2 x^2}$ - Where is the flaw?

Published on 14 Nov 2019 - 17:07

score 41 · Answer 9 · 2019-11-14 17:40:44

41

Views

Please verify my argument for $f_n(x)=x^n$ not uniformly convergent on $(0,1)$

Published on 14 Nov 2019 - 17:40

score 53 · Answer 10 · 2019-11-15 20:14:22

53

Views

Prove the existence of an $n'$ such as for all $n>n'$ : $\frac{U_{n+1}}{U_n} < 3/4$

Published on 15 Nov 2019 - 20:14

score 43 · Answer 11 · 2019-11-18 23:48:11

43

Views

$\lim_{m \to \infty}\lim_{n\to \infty}s_{m,n}=p$ implies that $\lim_{m \to \infty} s_{m,n_m}=p$

Published on 18 Nov 2019 - 23:48

score 105 · Answer 12 · 2026-02-23 08:36:04

105

Views

Equicontinuity + Compact $\rightarrow$ Uniform eqcontinuity

Published on 23 Feb 2026 - 8:36

score 61 · Answer 13 · 2026-02-23 07:02:29

61

Views

Show that $F=\{f_n\;|\; n\in N, \; f_n:[0,1]\to R \; \ni f_n(x)=x^n\}$ is not equicontinuous at $x=0$

Published on 23 Feb 2026 - 7:02

score 429 · Answer 14 · 2026-02-23 07:00:57

429

Views

Show that $\{\sin(nx) \; \mid \; n \in N\}$ is not equicontinuous at $x=1$

Published on 23 Feb 2026 - 7:00

score 283 · Answer 15 · 2019-11-22 19:05:01

283

Views

Evaluate the following limit: $\lim\limits_{h\to 0} \frac {1}{h} \int_2^{2+h}\sin(x^2) \, dx $

Published on 22 Nov 2019 - 19:05

List Question

What if the interval $[0,1]$ changes to $\mathbb R$ in the question?

If $(f_n)$ converges uniformly to $f$, then prove that $\lim_{x\to c}\lim_{n\to \infty} f_n(x) = \lim_{n\to \infty} \lim_{x\to c}f_n(x) $

Is it necessarily true for $(f_n)$ to converge uniformly on $[a,b]$

Show that $\{0,1\}^{[0,1]}$ is not sequentially compact

Calculating functional sequence

calculate the limit of a numerical sequence

Convergence of $g _ { n } ( x ) = \int _ { 0 } ^ { x }f_n(t)dt $

Uniform convergence of $f_n(x) = \frac{nx}{1+ n^2 x^2}$ - Where is the flaw?

Please verify my argument for $f_n(x)=x^n$ not uniformly convergent on $(0,1)$

Prove the existence of an $n'$ such as for all $n>n'$ : $\frac{U_{n+1}}{U_n} < 3/4$

$\lim_{m \to \infty}\lim_{n\to \infty}s_{m,n}=p$ implies that $\lim_{m \to \infty} s_{m,n_m}=p$

Equicontinuity + Compact $\rightarrow$ Uniform eqcontinuity

Show that $F=\{f_n\;|\; n\in N, \; f_n:[0,1]\to R \; \ni f_n(x)=x^n\}$ is not equicontinuous at $x=0$

Show that $\{\sin(nx) \; \mid \; n \in N\}$ is not equicontinuous at $x=1$

Evaluate the following limit: $\lim\limits_{h\to 0} \frac {1}{h} \int_2^{2+h}\sin(x^2) \, dx $

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