Question

How to Evaluate $\int_{0}^{\infty}\frac{x^2+2}{x^4+4} \ dx$ given $\mathcal{F}_c(e^{-x}\cos(x))=\sqrt{\frac{2}{\pi}}\frac{k^2+2}{k^4+4}$

score 48 · Answer 1 · 2026-04-15 06:59:46

48

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How to Evaluate $\int_{0}^{\infty}\frac{x^2+2}{x^4+4} \ dx$ given $\mathcal{F}_c(e^{-x}\cos(x))=\sqrt{\frac{2}{\pi}}\frac{k^2+2}{k^4+4}$

Published on 15 Apr 2026 - 6:59

score 98 · Answer 2 · 2026-04-15 18:05:35

98

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prove or disprove：$f'(x)$ can not be injective over $(a,b)$.

Published on 15 Apr 2026 - 18:05

score 61 · Answer 3 · 2026-04-14 21:49:40

61

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For an increasing function $f$, if $f(y_n)-f(x_n) \to 0$ , then $f$ is continuous at $0$

Published on 14 Apr 2026 - 21:49

score 1.1k · Answer 4 · 2026-04-13 19:36:22

1.1k

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Homeomorphism between upper closed hemisphere and disk.

Published on 13 Apr 2026 - 19:36

score 199 · Answer 5 · 2026-05-11 10:11:46

199

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If $R$ is a right-Noetherian ring and the Jacobson radical satisfies the right Artin-Rees property, then $\bigcap^{\infty}_{n=1}\text{Jac}(R)^n = 0$

Published on 11 May 2026 - 10:11

score 118 · Answer 6 · 2026-04-16 09:51:18

118

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If $f:[0,1]\to \mathbb{C} $ be continuous with $f(0)=0$ and $f(1)=2$, then $|f(t_0)|=1$ for some $t_0 \in [0,1]$

Published on 16 Apr 2026 - 9:51

score 103 · Answer 7 · 2026-04-13 08:50:18

103

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A linear transform mapping one billinear map to another may not exist (counter-example)

Published on 13 Apr 2026 - 8:50

score 1.1k · Answer 8 · 2026-04-13 21:00:47

1.1k

Views

Proof that every common divisor divides GCD (solve only by Bézout's identity)

Published on 13 Apr 2026 - 21:00

score 42 · Answer 9 · 2026-04-13 16:27:30

42

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Show that $\varphi: \overline{E} \times K \longrightarrow N$ is continuous

Published on 13 Apr 2026 - 16:27

score 305 · Answer 10 · 2026-04-17 12:53:12

305

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If $x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ $f_n (x_n) \rightarrow f(x)$ ,then $f_n \rightarrow f$ uniformly in each compact set $K $

Published on 17 Apr 2026 - 12:53

score 128 · Answer 11 · 2026-04-12 05:15:06

128

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How to use Wald's equation to determine expectation in gambling model?

Published on 12 Apr 2026 - 5:15

score 458 · Answer 12 · 2026-04-10 23:50:47

458

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Determining whether counting events is a renewal process

Published on 10 Apr 2026 - 23:50

score 108 · Answer 13 · 2026-04-13 21:49:01

108

Views

Let $S=\{x~|~x\in G$ and $x^2 \in H\}$. Show that $S$ is a subgroup of $G$ for $H<G$, $G$ abelian.

Published on 13 Apr 2026 - 21:49

score 1.3k · Answer 14 · 2026-04-08 18:12:18

1.3k

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Fourier Transform of Airy Equation

Published on 08 Apr 2026 - 18:12

score 110 · Answer 15 · 2026-04-30 04:00:35

110

Views

Jech Set Theory (3rd Edition) Exercise 7.16

Published on 30 Apr 2026 - 4:00

List Question

How to Evaluate $\int_{0}^{\infty}\frac{x^2+2}{x^4+4} \ dx$ given $\mathcal{F}_c(e^{-x}\cos(x))=\sqrt{\frac{2}{\pi}}\frac{k^2+2}{k^4+4}$

prove or disprove：$f'(x)$ can not be injective over $(a,b)$.

For an increasing function $f$, if $f(y_n)-f(x_n) \to 0$ , then $f$ is continuous at $0$

Homeomorphism between upper closed hemisphere and disk.

If $R$ is a right-Noetherian ring and the Jacobson radical satisfies the right Artin-Rees property, then $\bigcap^{\infty}_{n=1}\text{Jac}(R)^n = 0$

If $f:[0,1]\to \mathbb{C} $ be continuous with $f(0)=0$ and $f(1)=2$, then $|f(t_0)|=1$ for some $t_0 \in [0,1]$

A linear transform mapping one billinear map to another may not exist (counter-example)

Proof that every common divisor divides GCD (solve only by Bézout's identity)

Show that $\varphi: \overline{E} \times K \longrightarrow N$ is continuous

If $x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ $f_n (x_n) \rightarrow f(x)$ ,then $f_n \rightarrow f$ uniformly in each compact set $K $

How to use Wald's equation to determine expectation in gambling model?

Determining whether counting events is a renewal process

Let $S=\{x~|~x\in G$ and $x^2 \in H\}$. Show that $S$ is a subgroup of $G$ for $H<G$, $G$ abelian.

Fourier Transform of Airy Equation

Jech Set Theory (3rd Edition) Exercise 7.16

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