Question

Is the minimum of a sequence of uniformly equicontinuous functions continuous?

score 96 · Answer 1 · 2026-02-23 22:50:50

96

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Is the minimum of a sequence of uniformly equicontinuous functions continuous?

Published on 23 Feb 2026 - 22:50

score 55 · Answer 2 · 2026-02-26 01:21:08

55

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Pointwise convergence of this sequence $f_n: \mathbb{R}^+ \rightarrow \mathbb{R}$

Published on 26 Feb 2026 - 1:21

score 91 · Answer 3 · 2021-06-24 09:17:37

91

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Uniform convergence of $f_n(x)=\frac{n\cdot x}{1+n^2}$

Published on 24 Jun 2021 - 9:17

score 885 · Answer 4 · 2021-07-01 11:18:11

885

Views

Dini's Theorem Proof on the Reals

Published on 01 Jul 2021 - 11:18

score 67 · Answer 5 · 2021-07-06 03:09:55

67

Views

Not sure where my error is for integrating a sequence of functions

Published on 06 Jul 2021 - 3:09

score 57 · Answer 6 · 2021-07-06 18:04:14

57

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If $f(x,t)$ is of class $C^1$ then does $f_n(x):=\frac{f(x,t_n)-f(x,t_0)}{t_n-t_0}$ uniformly converge to $\frac{\partial f}{\partial t}(x,t_0)$?

Published on 06 Jul 2021 - 18:04

score 99 · Answer 7 · 2021-07-08 11:41:40

99

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For which values of $x$ the limit $\displaystyle\lim_{n\to \infty} (-1)^n \frac x{2^n}$ exists?

Published on 08 Jul 2021 - 11:41

score 72 · Answer 8 · 2026-02-26 01:17:25

72

Views

Recursive function converges to $e^t-t-1$

Published on 26 Feb 2026 - 1:17

score 58 · Answer 9 · 2021-07-15 04:29:46

58

Views

Given $x_{n+1}=x_n(1-x_n)$, find $\lim_{n \to \infty}n.x_{n}$

Published on 15 Jul 2021 - 4:29

score 80 · Answer 10 · 2021-07-15 20:28:31

80

Views

Integral of $L^{p}(\mathbb{R}^{n})$ sequence outside a large ball

Published on 15 Jul 2021 - 20:28

score 73 · Answer 11 · 2021-07-16 12:59:52

73

Views

Show that function series is bounded

Published on 16 Jul 2021 - 12:59

score 64 · Answer 12 · 2021-07-16 18:07:46

64

Views

$\sum_{n=1}^{\infty} | f_n(x)|<\infty$ a.e. $\Rightarrow$ $\lim_{N\to \infty}\sum_{n=1}^N f_n (x)$ exist (at least a.e.)

Published on 16 Jul 2021 - 18:07

score 49 · Answer 13 · 2021-07-23 22:56:28

49

Views

A sequence $x_n(t)\in C^1[0,1]$ with $x(0)=0$ such that $x_n(t)\to x(t)$ in $C[0,1]$ and $x'_n(t)\to y(t)$ in $L^2[0,1]$ but $x'(t)\neq y(t)$

Published on 23 Jul 2021 - 22:56

score 34 · Answer 14 · 2021-07-28 11:12:44

34

Views

Integral of polynomials & $f_k(x) = \begin{cases} 2k& x \in[\frac{-1}{k},\frac{1}{k}] \\ 0&x \in[-1,1]\setminus[\frac{-1}{k},\frac{1}{k}] \end{cases}$

Published on 28 Jul 2021 - 11:12

score 164 · Answer 15 · 2021-07-29 11:55:37

164

Views

Find a formula for this sequence of integer-valued polynomials

Published on 29 Jul 2021 - 11:55

List Question

Is the minimum of a sequence of uniformly equicontinuous functions continuous?

Pointwise convergence of this sequence $f_n: \mathbb{R}^+ \rightarrow \mathbb{R}$

Uniform convergence of $f_n(x)=\frac{n\cdot x}{1+n^2}$

Dini's Theorem Proof on the Reals

Not sure where my error is for integrating a sequence of functions

If $f(x,t)$ is of class $C^1$ then does $f_n(x):=\frac{f(x,t_n)-f(x,t_0)}{t_n-t_0}$ uniformly converge to $\frac{\partial f}{\partial t}(x,t_0)$?

For which values of $x$ the limit $\displaystyle\lim_{n\to \infty} (-1)^n \frac x{2^n}$ exists?

Recursive function converges to $e^t-t-1$

Given $x_{n+1}=x_n(1-x_n)$, find $\lim_{n \to \infty}n.x_{n}$

Integral of $L^{p}(\mathbb{R}^{n})$ sequence outside a large ball

Show that function series is bounded

$\sum_{n=1}^{\infty} | f_n(x)|<\infty$ a.e. $\Rightarrow$ $\lim_{N\to \infty}\sum_{n=1}^N f_n (x)$ exist (at least a.e.)

A sequence $x_n(t)\in C^1[0,1]$ with $x(0)=0$ such that $x_n(t)\to x(t)$ in $C[0,1]$ and $x'_n(t)\to y(t)$ in $L^2[0,1]$ but $x'(t)\neq y(t)$

Integral of polynomials & $f_k(x) = \begin{cases} 2k& x \in[\frac{-1}{k},\frac{1}{k}] \\ 0&x \in[-1,1]\setminus[\frac{-1}{k},\frac{1}{k}] \end{cases}$

Find a formula for this sequence of integer-valued polynomials

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