List questions from real-analysis

Published on 17 Apr 2026 - 8:59

118

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Integrating $\int_{0}^{1} x^a (1-x)^b (1-2x)^c \, \mathrm dx $

Published on 20 Apr 2026 - 2:59

58

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Sequence of continuous function that converges pointwise

Published on 17 Apr 2026 - 9:57

414

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Show that uniform limit of sequence of Baire $1$ functions is Baire $1$

Published on 16 Apr 2026 - 8:11

91

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Ramanujan’s puzzling problem

Published on 12 Apr 2026 - 23:54

53

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An exercise on the derivation of distributions: $\frac{d^m}{dx^m} \Big( H(x) \frac {x^{m-1}}{(m-1)!}\Big)$

Published on 15 Apr 2026 - 18:00

182

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Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$

Published on 27 Mar 2026 - 13:25

132

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Prove that $a_n=\sqrt[n]{f\left(\frac{1}{n} \right)^n+f\left(\frac{2}{n} \right)^n+\dots+f\left(\frac{n}{n} \right)^n}$ is convergent

Published on 16 Apr 2026 - 23:19

120

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The supremum of a continuous mapping

Published on 13 Apr 2026 - 6:02

40

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Real analysis of intermediate value property

Published on 10 Apr 2026 - 17:48

3.4k

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Heat equation - Step function initial condition

Published on 14 Apr 2026 - 7:14

117

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proving that $\lim_{x \to \pi} \frac{1+\cos x }{1+\cos 3x}=\frac{1}{9}$ without L'Hôpital.

Published on 15 Apr 2026 - 21:20

90

Views

Understanding limit superior of a sequence

Published on 12 Apr 2026 - 15:10

133

Views

Understanding why $\mathbb{R}^2$ is complete

Published on 23 Apr 2026 - 5:17

1k

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A set $S \subset \mathbb{R}$ has no cluster points iff $S \cap [-n,n]$ is a finite set for each $n \geq 1$

Published on 15 Apr 2026 - 4:07

List Question

$\cos(\cos(\cdots(\cos(x))\cdots))$

Integrating $\int_{0}^{1} x^a (1-x)^b (1-2x)^c \, \mathrm dx $

Sequence of continuous function that converges pointwise

Show that uniform limit of sequence of Baire $1$ functions is Baire $1$

Ramanujan’s puzzling problem

An exercise on the derivation of distributions: $\frac{d^m}{dx^m} \Big( H(x) \frac {x^{m-1}}{(m-1)!}\Big)$

Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$

Prove that $a_n=\sqrt[n]{f\left(\frac{1}{n} \right)^n+f\left(\frac{2}{n} \right)^n+\dots+f\left(\frac{n}{n} \right)^n}$ is convergent

The supremum of a continuous mapping

Real analysis of intermediate value property

Heat equation - Step function initial condition

proving that $\lim_{x \to \pi} \frac{1+\cos x }{1+\cos 3x}=\frac{1}{9}$ without L'Hôpital.

Understanding limit superior of a sequence

Understanding why $\mathbb{R}^2$ is complete

A set $S \subset \mathbb{R}$ has no cluster points iff $S \cap [-n,n]$ is a finite set for each $n \geq 1$

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