List questions from real-analysis

Published on 17 Apr 2026 - 14:44

758

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Let $A$ and $B$ be a non-empty subsets of $\mathbb{R}$ suppose that $a \leq b$ for every $a\in A$ and for every $b\in B$

Published on 16 Apr 2026 - 13:29

241

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Convergence of $\sum_{n=1}^\infty \frac{\sqrt[n]{n} - 1}{n}$

Published on 14 Apr 2026 - 14:02

40

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Showing that $F(x)= \int^{b(x)}_{a(x)}f(x,t)dt$ is derivable.

Published on 11 Apr 2026 - 16:52

707

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Is an integral itself a function or a constant?

Published on 11 Apr 2026 - 4:01

140

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Gagliardo-Niremberg inequality on annuli (proof)

Published on 14 Apr 2026 - 3:07

43

Views

Two questions concerning series involving the Möbius function and trigonometric functions

Published on 23 Apr 2026 - 7:53

95

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Confusion about convex function on compact set

Published on 24 Mar 2026 - 22:06

133

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Is what I have got about $\int\sqrt{x+\left(\sqrt{{x}+\sqrt{x+\cdots}}\right)}dx$ true or false?

Published on 19 Apr 2026 - 23:02

62

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$L_2$ integrability of function composition

Published on 17 Apr 2026 - 0:04

61

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How can we show that $y_n=z_n$?

Published on 14 Apr 2026 - 0:54

127

Views

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

Published on 20 Apr 2026 - 13:22

67

Views

Sum of a series involving integral

Published on 13 Apr 2026 - 15:42

1.3k

Views

Provided $f$ is continuous at $x_0$, and $f(x+y) = f(x) + f(y)$ prove $f$ is continuous everywhere.

Published on 14 Apr 2026 - 13:44

5.9k

Views

Estimate the $L^1$-norm of the Fourier transform

Published on 14 Apr 2026 - 21:16

List Question

Find limit of $\lim_{x\to 0}{\left(\sqrt{x^6+5x^4+7x^2}\cos(1+x^{-1000})\right)}$, if it exists

Let $A$ and $B$ be a non-empty subsets of $\mathbb{R}$ suppose that $a \leq b$ for every $a\in A$ and for every $b\in B$

Convergence of $\sum_{n=1}^\infty \frac{\sqrt[n]{n} - 1}{n}$

Showing that $F(x)= \int^{b(x)}_{a(x)}f(x,t)dt$ is derivable.

Is an integral itself a function or a constant?

Gagliardo-Niremberg inequality on annuli (proof)

Two questions concerning series involving the Möbius function and trigonometric functions

Confusion about convex function on compact set

Is what I have got about $\int\sqrt{x+\left(\sqrt{{x}+\sqrt{x+\cdots}}\right)}dx$ true or false?

$L_2$ integrability of function composition

How can we show that $y_n=z_n$?

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

Sum of a series involving integral

Provided $f$ is continuous at $x_0$, and $f(x+y) = f(x) + f(y)$ prove $f$ is continuous everywhere.

Estimate the $L^1$-norm of the Fourier transform

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