Question

$\lim_n \frac{1}{n}\int_{1/n^2}^{+\infty} \frac{\tanh(\frac{\sqrt{x}}{n})}{x^2\sqrt{(n+1)x}}\ dx$

score 53 · Answer 1 · 2020-05-03 16:57:20

53

Views

$\lim_n \frac{1}{n}\int_{1/n^2}^{+\infty} \frac{\tanh(\frac{\sqrt{x}}{n})}{x^2\sqrt{(n+1)x}}\ dx$

Published on 03 May 2020 - 16:57

score 132 · Answer 2 · 2020-05-04 22:45:38

132

Views

let $p$ be a real non-constant polynomial, prove that $\lim_{n \to \infty}\int_{0}^{1} e^{2\pi i n p(x)}dx=0$.

Published on 04 May 2020 - 22:45

score 46 · Answer 3 · 2026-03-25 06:28:03

46

Views

Expected value of countable sum of i.i.d. standard normal random variables

Published on 25 Mar 2026 - 6:28

score 144 · Answer 4 · 2020-05-05 03:26:26

144

Views

Prove The Identity Using Tonelli's or Fubini's Theorem

Published on 05 May 2020 - 3:26

score 203 · Answer 5 · 2020-05-05 07:26:30

203

Views

Laplace Transformation for measurable functions

Published on 05 May 2020 - 7:26

score 170 · Answer 6 · 2020-05-05 19:37:19

170

Views

If $g:[a,b]\to[0,\infty]$ is lebesgue integrable on the compact interval $[a,b]$, is $g$ bounded $\textit{almost everywhere}$?

Published on 05 May 2020 - 19:37

score 242 · Answer 7 · 2020-05-05 19:45:21

242

Views

Show that if $\int fh < \infty$ for all $h \in L^q$ then $f \in L^p$

Published on 05 May 2020 - 19:45

score 43 · Answer 8 · 2020-05-06 03:06:55

43

Views

Let $f_n \in L^2[0,1]$ and $\|f_n\|_2=1$ and suppose $\lim_{m,n \to \infty}\|f_m+f_n\|_2=2$, prove that there is $f \in L^2$ s.t $f_n \to f$ in $L^2$

Published on 06 May 2020 - 3:06

score 75 · Answer 9 · 2020-05-06 04:24:54

75

Views

Let $f \in L^1(\mathbb{R})$ and $\|f\|_1=1$, show that for $\delta>0$ $\lim_{n \to \infty}\int_{|x|\geq \delta}nf(nx)dx=0$

Published on 06 May 2020 - 4:24

score 30 · Answer 10 · 2020-05-06 12:11:14

30

Views

Is this inequality in $L^p(\Omega)$ true?

Published on 06 May 2020 - 12:11

score 35 · Answer 11 · 2020-05-06 12:16:21

35

Views

Integral inequality in $L^p(\Omega)$

Published on 06 May 2020 - 12:16

score 90 · Answer 12 · 2020-05-06 23:59:55

90

Views

Is $F(x)=\int_{\mathbb{R}}f(t)\frac{\sin(xt)}{t}dt$ differentiable for $f\in L^1$

Published on 06 May 2020 - 23:59

score 84 · Answer 13 · 2020-05-07 18:57:06

84

Views

Prove $f(x)=\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is Improper Riemann Integrable

Published on 07 May 2020 - 18:57

score 281 · Answer 14 · 2026-03-25 13:57:51

281

Views

Equivalence of Hausdorff and Spherical measure on $\mathbb{S}^{n}$

Published on 25 Mar 2026 - 13:57

score 185 · Answer 15 · 2020-05-08 02:48:47

185

Views

If $f_n\leq g_n \leq h_n$, $f_n \to f$, $h_n \to h$ pointwise and $\int f_n\to\int f$,$\int h_n \to \int h$ then prove that $\int g_n \to \int g$

Published on 08 May 2020 - 2:48

List Question

$\lim_n \frac{1}{n}\int_{1/n^2}^{+\infty} \frac{\tanh(\frac{\sqrt{x}}{n})}{x^2\sqrt{(n+1)x}}\ dx$

let $p$ be a real non-constant polynomial, prove that $\lim_{n \to \infty}\int_{0}^{1} e^{2\pi i n p(x)}dx=0$.

Expected value of countable sum of i.i.d. standard normal random variables

Prove The Identity Using Tonelli's or Fubini's Theorem

Laplace Transformation for measurable functions

If $g:[a,b]\to[0,\infty]$ is lebesgue integrable on the compact interval $[a,b]$, is $g$ bounded $\textit{almost everywhere}$?

Show that if $\int fh < \infty$ for all $h \in L^q$ then $f \in L^p$

Let $f_n \in L^2[0,1]$ and $\|f_n\|_2=1$ and suppose $\lim_{m,n \to \infty}\|f_m+f_n\|_2=2$, prove that there is $f \in L^2$ s.t $f_n \to f$ in $L^2$

Let $f \in L^1(\mathbb{R})$ and $\|f\|_1=1$, show that for $\delta>0$ $\lim_{n \to \infty}\int_{|x|\geq \delta}nf(nx)dx=0$

Is this inequality in $L^p(\Omega)$ true?

Integral inequality in $L^p(\Omega)$

Is $F(x)=\int_{\mathbb{R}}f(t)\frac{\sin(xt)}{t}dt$ differentiable for $f\in L^1$

Prove $f(x)=\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is Improper Riemann Integrable

Equivalence of Hausdorff and Spherical measure on $\mathbb{S}^{n}$

If $f_n\leq g_n \leq h_n$, $f_n \to f$, $h_n \to h$ pointwise and $\int f_n\to\int f$,$\int h_n \to \int h$ then prove that $\int g_n \to \int g$

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