Question

Show that $\lim_{n\rightarrow \infty}\int_{a}^{\pi/2}\sqrt{n} \cos^n(x)dx=0$ for any $a\in \left(0,\frac{\pi}{2}\right)$

score 133 · Answer 1 · 2018-08-21 14:02:54

133

Views

Show that $\lim_{n\rightarrow \infty}\int_{a}^{\pi/2}\sqrt{n} \cos^n(x)dx=0$ for any $a\in \left(0,\frac{\pi}{2}\right)$

Published on 21 Aug 2018 - 14:02

score 37 · Answer 2 · 2018-08-21 21:32:43

37

Views

Prove that $\sum_{k=1}^{\infty} a_k g(x-r_k) \not\in L^2(\mathbb{R})$

Published on 21 Aug 2018 - 21:32

score 705 · Answer 3 · 2026-03-25 09:33:41

705

Views

An integral about radial function.

Published on 25 Mar 2026 - 9:33

score 89 · Answer 4 · 2018-08-23 21:10:52

89

Views

Exchange of limit and integral

Published on 23 Aug 2018 - 21:10

score 106 · Answer 5 · 2018-08-24 15:48:57

106

Views

Showing that $\frac{x}{(x^2+y^2)^2}$ is locally integrable

Published on 24 Aug 2018 - 15:48

score 99 · Answer 6 · 2018-08-24 22:56:27

99

Views

Lebesgue integrability of $\sum_{n=1}^\infty f_n(x)$, where $f_n(x):=ae^{-anx}-be^{-bnx}$

Published on 24 Aug 2018 - 22:56

score 420 · Answer 7 · 2018-08-26 21:20:04

420

Views

Evaluating improper double integral with Lebesgue

Published on 26 Aug 2018 - 21:20

score 76 · Answer 8 · 2018-08-27 19:00:55

76

Views

Define $L_2(\Omega)$ as the completion of $C_c(\Omega)$ in scalar product norm

Published on 27 Aug 2018 - 19:00

score 86 · Answer 9 · 2018-08-29 10:31:53

86

Views

An unbounded function with integrability for all p>0

Published on 29 Aug 2018 - 10:31

score 111 · Answer 10 · 2018-08-30 15:01:28

111

Views

Lebesgue Dominated Convergence Application

Published on 30 Aug 2018 - 15:01

score 140 · Answer 11 · 2018-08-31 07:42:03

140

Views

Integral of 1-form along any path between two points

Published on 31 Aug 2018 - 7:42

score 39 · Answer 12 · 2018-08-31 16:46:57

39

Views

Iterated Integral not replicable

Published on 31 Aug 2018 - 16:46

score 891 · Answer 13 · 2018-08-31 16:55:32

891

Views

Integral with respect to the sum of two complex measures

Published on 31 Aug 2018 - 16:55

score 59 · Answer 14 · 2018-09-02 19:11:08

59

Views

Given a sequence of functions, I wish to prove the existence of $f\in L^1(\mathbb{R})$ such that...

Published on 02 Sep 2018 - 19:11

score 65 · Answer 15 · 2018-09-03 17:02:00

65

Views

What does $f\in L^p(\partial \Omega )$ mean

Published on 03 Sep 2018 - 17:02

List Question

Show that $\lim_{n\rightarrow \infty}\int_{a}^{\pi/2}\sqrt{n} \cos^n(x)dx=0$ for any $a\in \left(0,\frac{\pi}{2}\right)$

Prove that $\sum_{k=1}^{\infty} a_k g(x-r_k) \not\in L^2(\mathbb{R})$

An integral about radial function.

Exchange of limit and integral

Showing that $\frac{x}{(x^2+y^2)^2}$ is locally integrable

Lebesgue integrability of $\sum_{n=1}^\infty f_n(x)$, where $f_n(x):=ae^{-anx}-be^{-bnx}$

Evaluating improper double integral with Lebesgue

Define $L_2(\Omega)$ as the completion of $C_c(\Omega)$ in scalar product norm

An unbounded function with integrability for all p>0

Lebesgue Dominated Convergence Application

Integral of 1-form along any path between two points

Iterated Integral not replicable

Integral with respect to the sum of two complex measures

Given a sequence of functions, I wish to prove the existence of $f\in L^1(\mathbb{R})$ such that...

What does $f\in L^p(\partial \Omega )$ mean

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