Question

Proving $\int_0^1\frac{dx}{[ax+b(1-x)]^2}=\frac1{ab}$

score 296 · Answer 1 · 2026-04-08 22:36:26

296

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Proving $\int_0^1\frac{dx}{[ax+b(1-x)]^2}=\frac1{ab}$

Published on 08 Apr 2026 - 22:36

score 1.3k · Answer 2 · 2026-04-10 19:48:58

1.3k

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Intuition on Axiom of Completeness (Lower Bounds)

Published on 10 Apr 2026 - 19:48

score 179 · Answer 3 · 2026-04-08 23:12:18

179

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If $u\in W^{1,p}(\Omega )$ is s.t. $\nabla u=0$ then $u$ is constant a.e.

Published on 08 Apr 2026 - 23:12

score 458 · Answer 4 · 2026-04-10 02:54:51

458

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Cut Property Implies Completeness Proof

Published on 10 Apr 2026 - 2:54

score 146 · Answer 5 · 2026-04-08 22:49:26

146

Views

Distributional solution of differential equation

Published on 08 Apr 2026 - 22:49

score 412 · Answer 6 · 2026-04-09 23:20:18

412

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Proving the sharper form of the Lebesgue Differentiation Theorem

Published on 09 Apr 2026 - 23:20

score 103 · Answer 7 · 2026-04-08 23:10:39

103

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If $A\subseteq(0,+\infty)$ is nonempty and closed under addition then it is not bounded above.

Published on 08 Apr 2026 - 23:10

score 183 · Answer 8 · 2026-04-10 02:54:50

183

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Prove that $f(x)= \begin{cases} \frac{x+1}{e^{2x}+1}, & x≠0 \\ 1/2, & x=0 \end{cases}$ is continuous and differentiable.

Published on 10 Apr 2026 - 2:54

score 59 · Answer 9 · 2018-01-15 19:43:42

Let $X\subseteq \mathbb R_{>0}$ be uncountable. Prove there is a countable subset $S$ of$ X$, such that $\sum_{x\in S} x=\infty$

score 281 · Answer 10 · 2026-04-10 10:25:18

281

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Why the approximate solution of $\frac{1}{{\sqrt {2\pi } }}\frac{n}{x}{e^{ - \frac{{{x^2}}}{2}}} = c$ is $\sqrt {2\log n} $ when $n$ is large

Published on 10 Apr 2026 - 10:25

score 40 · Answer 11 · 2026-04-10 03:19:40

40

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Show that $\mathcal{F} = \{E, E_1, E_2, E_3 \}$ is a $\sigma$-algebra.

Published on 10 Apr 2026 - 3:19

score 75 · Answer 12 · 2026-04-10 03:11:08

75

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Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?

Published on 10 Apr 2026 - 3:11

score 421 · Answer 13 · 2026-04-05 20:05:24

421

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Interior Points and Openness

Published on 05 Apr 2026 - 20:05

score 1k · Answer 14 · 2026-04-09 01:51:00

1k

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Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi

Published on 09 Apr 2026 - 1:51

score 101 · Answer 15 · 2026-03-24 19:08:59

101

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Somewhat shady way of solving a problem from Baby Rudin

Published on 24 Mar 2026 - 19:08

List Question

Proving $\int_0^1\frac{dx}{[ax+b(1-x)]^2}=\frac1{ab}$

Intuition on Axiom of Completeness (Lower Bounds)

If $u\in W^{1,p}(\Omega )$ is s.t. $\nabla u=0$ then $u$ is constant a.e.

Cut Property Implies Completeness Proof

Distributional solution of differential equation

Proving the sharper form of the Lebesgue Differentiation Theorem

If $A\subseteq(0,+\infty)$ is nonempty and closed under addition then it is not bounded above.

Prove that $f(x)= \begin{cases} \frac{x+1}{e^{2x}+1}, & x≠0 \\ 1/2, & x=0 \end{cases}$ is continuous and differentiable.

Let $X\subseteq \mathbb R_{>0}$ be uncountable. Prove there is a countable subset $S$ of$ X$, such that $\sum_{x\in S} x=\infty$

Why the approximate solution of $\frac{1}{{\sqrt {2\pi } }}\frac{n}{x}{e^{ - \frac{{{x^2}}}{2}}} = c$ is $\sqrt {2\log n} $ when $n$ is large

Show that $\mathcal{F} = \{E, E_1, E_2, E_3 \}$ is a $\sigma$-algebra.

Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?

Interior Points and Openness

Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi

Somewhat shady way of solving a problem from Baby Rudin

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