Question

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

score 73 · Answer 1 · 2026-04-17 11:42:12

73

Views

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

Published on 17 Apr 2026 - 11:42

score 507 · Answer 2 · 2026-04-11 05:40:55

507

Views

Chain rule for higher Fréchet derivatives?

Published on 11 Apr 2026 - 5:40

score 443 · Answer 3 · 2026-04-12 21:05:42

443

Views

$A \subseteq \mathbb{R}^{2}$ is not homeomorphic to an open subset of $\mathbb{R^{n}}$, $n\geq 3$

Published on 12 Apr 2026 - 21:05

score 67 · Answer 4 · 2026-04-19 16:53:27

67

Views

Limit of $y=f(x)=\frac{3x-e^{\sin x}}{5+e^{-x}-\cos x}$

Published on 19 Apr 2026 - 16:53

score 51 · Answer 5 · 2026-04-16 12:33:48

51

Views

$\rho=\sqrt{\frac{R+j \omega L}{G+j \omega C}}$, find the condition to have $Re\{\rho\}\ge0$ and $Im\{\rho\}\ge0$

Published on 16 Apr 2026 - 12:33

score 99 · Answer 6 · 2026-04-17 14:52:34

99

Views

Solving double integral $\iint_A \frac{\tan(x+y)}{x+y}dxdy$

Published on 17 Apr 2026 - 14:52

score 191 · Answer 7 · 2026-04-17 09:17:37

191

Views

How to prove that $1+\frac11(1+\frac12(1+\frac13(...(1+\frac1{n-1}(1+\frac1n))...)))=1+\frac1{1!}+\frac1{2!}+\frac1{3!}+...+\frac1{n!}$?

Published on 17 Apr 2026 - 9:17

score 131 · Answer 8 · 2026-04-15 13:24:23

131

Views

If $f$ is Hölder continuous, are we able to conclude that $(t,x)\mapsto\int_0^tf(x+sh)\:{\rm d}s$ is Hölder continuous?

Published on 15 Apr 2026 - 13:24

score 43 · Answer 9 · 2026-04-15 13:04:15

43

Views

Area preservation when transverse intersection

Published on 15 Apr 2026 - 13:04

score 174 · Answer 10 · 2026-04-14 16:58:06

174

Views

Why is a continuously differentiable function on a domain already holomorphic when it is holomorphic on a dense subset?

Published on 14 Apr 2026 - 16:58

score 94 · Answer 11 · 2026-04-15 08:20:38

94

Views

Calculate $\int_S \vec{A} \cdot \hat{n} \ dS, S=\{x^2+y^2+z^2=R^2, z \ge 0\}$

Published on 15 Apr 2026 - 8:20

score 85 · Answer 12 · 2026-04-15 22:50:28

85

Views

Qualitative analysis of $y' = \frac {(y+1) \cdot \sinh(x)}{(y+1) \cdot \log(y+1) +y}$

Published on 15 Apr 2026 - 22:50

score 467 · Answer 13 · 2026-04-13 04:57:39

467

Views

Alternate proof for weighted alternating shifted central binomial sum relation

Published on 13 Apr 2026 - 4:57

score 47 · Answer 14 · 2026-04-13 14:35:42

47

Views

Application of the mean value inequality

Published on 13 Apr 2026 - 14:35

score 124 · Answer 15 · 2026-04-17 09:32:34

124

Views

An alternative proof for $D_2 D_1 f(x) = D_1 D_2 f(x)$ when $f \in C^2$

Published on 17 Apr 2026 - 9:32

List Question

$\lim_{\epsilon\rightarrow 0^{+}}{\int_{0}^{\infty}\,e^{-\epsilon x}\,\frac{|\sin{x}|^{t}} {x^{t-1}}\,dx}, \quad 1< t<2$

Chain rule for higher Fréchet derivatives?

$A \subseteq \mathbb{R}^{2}$ is not homeomorphic to an open subset of $\mathbb{R^{n}}$, $n\geq 3$

Limit of $y=f(x)=\frac{3x-e^{\sin x}}{5+e^{-x}-\cos x}$

$\rho=\sqrt{\frac{R+j \omega L}{G+j \omega C}}$, find the condition to have $Re\{\rho\}\ge0$ and $Im\{\rho\}\ge0$

Solving double integral $\iint_A \frac{\tan(x+y)}{x+y}dxdy$

How to prove that $1+\frac11(1+\frac12(1+\frac13(...(1+\frac1{n-1}(1+\frac1n))...)))=1+\frac1{1!}+\frac1{2!}+\frac1{3!}+...+\frac1{n!}$?

If $f$ is Hölder continuous, are we able to conclude that $(t,x)\mapsto\int_0^tf(x+sh)\:{\rm d}s$ is Hölder continuous?

Area preservation when transverse intersection

Why is a continuously differentiable function on a domain already holomorphic when it is holomorphic on a dense subset?

Calculate $\int_S \vec{A} \cdot \hat{n} \ dS, S=\{x^2+y^2+z^2=R^2, z \ge 0\}$

Qualitative analysis of $y' = \frac {(y+1) \cdot \sinh(x)}{(y+1) \cdot \log(y+1) +y}$

Alternate proof for weighted alternating shifted central binomial sum relation

Application of the mean value inequality

An alternative proof for $D_2 D_1 f(x) = D_1 D_2 f(x)$ when $f \in C^2$

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