Question

Showing that the given sequence of functions converges to a given function on the given set as follows

score 37 · Answer 1 · 2022-02-11 14:23:07

Showing that the given sequence of functions converges to a given function on the given set as follows

Published on 11 Feb 2022 - 14:23

score 60 · Answer 2 · 2022-02-14 04:21:13

Showing that the sequence of functions defined by $f_n(x):=\frac{n^2x+n}{n^2+n+1}$ for all $x \in \Bbb R$ and $n \in \Bbb N$ is converges to $g(x)=x$

score 43 · Answer 3 · 2022-02-17 17:20:34

43

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Nonincreasing sequence of functions

Published on 17 Feb 2022 - 17:20

score 60 · Answer 4 · 2026-02-23 23:21:43

60

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Extraction of pointwise convergenct subsequence using Arzela-Ascoli theorem

Published on 23 Feb 2026 - 23:21

score 74 · Answer 5 · 2022-02-20 13:21:01

74

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Find $\sum f_n(x)$

Published on 20 Feb 2022 - 13:21

score 150 · Answer 6 · 2022-02-26 10:29:18

150

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Sequence of functions $f_n(x) = \frac{\sin nx}{1+nx}$ converges to $0$.

Published on 26 Feb 2022 - 10:29

score 89 · Answer 7 · 2026-02-26 07:58:21

89

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Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

Published on 26 Feb 2026 - 7:58

score 29 · Answer 8 · 2022-02-28 13:57:16

29

Views

Show that the sequence of functions $(f_n)$ is bounded uniformly.

Published on 28 Feb 2022 - 13:57

score 57 · Answer 9 · 2022-03-07 07:02:36

57

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Find the $\lim\limits_{n \to \infty} \int_{0}^{1}g_n(x)dx$ for these functions

Published on 07 Mar 2022 - 7:02

score 125 · Answer 10 · 2026-02-24 02:07:25

125

Views

Prove that the sequence of functions $f_n$ is equicontinuos, but with not uniformly convergent subsequence in $(0,1)$.

Published on 24 Feb 2026 - 2:07

score 37 · Answer 11 · 2022-03-09 00:56:04

37

Views

Does this proof of the Boundedness Theorem contain a mistake?

Published on 09 Mar 2022 - 0:56

score 43 · Answer 12 · 2022-03-12 16:13:51

43

Views

Proving that $B(E)$ is closed subalgebra of $C(K,\mathbb{C})$

Published on 12 Mar 2022 - 16:13

score 34 · Answer 13 · 2022-03-12 17:27:38

34

Views

Sequence of continuous functions $f_n $ with $\lim_{n \rightarrow +\infty} f_n(x)=f(x)$ and property

Published on 12 Mar 2022 - 17:27

score 42 · Answer 14 · 2022-03-13 14:04:29

42

Views

Prove sequence $B[t]=\sum_{k=1}^{t}\sum_{i=1}^{k}S[i]$ for $S=\{0,1\}^T$ contains at most one element equal to $1$ at the same index as in $S$

Published on 13 Mar 2022 - 14:04

score 53 · Answer 15 · 2022-03-19 16:10:51

53

Views

Choice of $N$ for $\frac{nx}{1+nx^2}$

Published on 19 Mar 2022 - 16:10

List Question

Showing that the given sequence of functions converges to a given function on the given set as follows

Showing that the sequence of functions defined by $f_n(x):=\frac{n^2x+n}{n^2+n+1}$ for all $x \in \Bbb R$ and $n \in \Bbb N$ is converges to $g(x)=x$

Nonincreasing sequence of functions

Extraction of pointwise convergenct subsequence using Arzela-Ascoli theorem

Find $\sum f_n(x)$

Sequence of functions $f_n(x) = \frac{\sin nx}{1+nx}$ converges to $0$.

Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

Show that the sequence of functions $(f_n)$ is bounded uniformly.

Find the $\lim\limits_{n \to \infty} \int_{0}^{1}g_n(x)dx$ for these functions

Prove that the sequence of functions $f_n$ is equicontinuos, but with not uniformly convergent subsequence in $(0,1)$.

Does this proof of the Boundedness Theorem contain a mistake?

Proving that $B(E)$ is closed subalgebra of $C(K,\mathbb{C})$

Sequence of continuous functions $f_n $ with $\lim_{n \rightarrow +\infty} f_n(x)=f(x)$ and property

Prove sequence $B[t]=\sum_{k=1}^{t}\sum_{i=1}^{k}S[i]$ for $S=\{0,1\}^T$ contains at most one element equal to $1$ at the same index as in $S$

Choice of $N$ for $\frac{nx}{1+nx^2}$

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