List questions from sequence-of-function

Published on 09 Mar 2020 - 14:05

67

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What is $\lim_{n\to \infty}\log(|\sin(\frac{1}{n})|)/\log(n+1)$

Published on 12 Mar 2020 - 3:01

116

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Show that the following equality holds for all $\alpha > 0$ but not for $\alpha = 0.$

Published on 14 Mar 2020 - 16:10

32

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an example where $ \phi (x) = \sup_{n \in Z^+} f_n(x)$ is not continuous.

Published on 23 Feb 2026 - 10:18

61

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The definition of a function series

Published on 15 Mar 2020 - 15:03

99

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Does the series $\sum_{n=0}^{\infty }\frac{1}{n+n^2x^2}$ converge uniformly on $x\in(a,\infty )\; a\geq 0$

Published on 18 Mar 2020 - 9:02

25

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$\sum_{1}^{\infty }\frac{1}{((n-1)x+1)(nx+1)}$ converges uniformly on $[1,\infty)$?

Published on 18 Mar 2020 - 10:58

29

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Uniform convergence of $g_n(z) = \log(|f_n(z)|)/\log(n+1)$ when $f_n(z) \to f(z)$ uniformly.

Published on 19 Mar 2020 - 5:42

87

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Asymptotic behaviour of a sequence of integrals

Published on 20 Mar 2020 - 14:11

18

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Convergence of a sequence of distribution obtained by application of Bayes theorem

Published on 23 Mar 2020 - 0:23

294

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How to find general form of sequence?

Published on 26 Mar 2020 - 0:49

150

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Uniform convergence of $\sum\limits_{n=1}^{\infty}{\frac{x^{n}}{100+x^{2n}}}$

Published on 26 Mar 2020 - 21:15

56

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Uniform Convergence for $\sum\limits_{n=1}^{\infty}{\frac{x^{n}}{100+x^{2n}}}$

Published on 27 Mar 2020 - 0:23

838

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Which of the following are uniformly continuous?

Published on 27 Mar 2020 - 5:57

197

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Show that $f_n$ converges uniformly to some continuous function $f(x)$ defined in R.

Published on 27 Mar 2020 - 16:18

List Question

Asymptotic behaviour of a sequence of functions

What is $\lim_{n\to \infty}\log(|\sin(\frac{1}{n})|)/\log(n+1)$

Show that the following equality holds for all $\alpha > 0$ but not for $\alpha = 0.$

an example where $ \phi (x) = \sup_{n \in Z^+} f_n(x)$ is not continuous.

The definition of a function series

Does the series $\sum_{n=0}^{\infty }\frac{1}{n+n^2x^2}$ converge uniformly on $x\in(a,\infty )\; a\geq 0$

$\sum_{1}^{\infty }\frac{1}{((n-1)x+1)(nx+1)}$ converges uniformly on $[1,\infty)$?

Uniform convergence of $g_n(z) = \log(|f_n(z)|)/\log(n+1)$ when $f_n(z) \to f(z)$ uniformly.

Asymptotic behaviour of a sequence of integrals

Convergence of a sequence of distribution obtained by application of Bayes theorem

How to find general form of sequence?

Uniform convergence of $\sum\limits_{n=1}^{\infty}{\frac{x^{n}}{100+x^{2n}}}$

Uniform Convergence for $\sum\limits_{n=1}^{\infty}{\frac{x^{n}}{100+x^{2n}}}$

Which of the following are uniformly continuous?

Show that $f_n$ converges uniformly to some continuous function $f(x)$ defined in R.

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