List questions from real-analysis

Published on 18 Apr 2026 - 9:22

414

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What is the value of $f(100)$?

Published on 13 Apr 2026 - 19:28

69

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Notation for a function with the domain $1$ or $0$?

Published on 17 Apr 2026 - 13:34

117

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On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

Published on 17 Apr 2026 - 2:36

989

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Is this an example of a pointwise convergent sequence of function but not uniformly convergent

Published on 13 Apr 2026 - 20:17

872

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Density of Lipschitz functions in the set of uniformly continuous functions

Published on 17 Apr 2026 - 19:55

94

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An inequality deduced for $-\sum_{n=1}^\infty\frac{\mu(n)}{n}x^{n-1}$ on assumption of convexity, invoking a theorem due to Dragomir

Published on 25 Apr 2026 - 2:46

86

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show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

Published on 15 Apr 2026 - 18:35

232

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How to integrate $\int{\frac{x^2+5}{x^3+3x}}dx$

Published on 25 Apr 2026 - 4:48

1.8k

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Intersection of compact subsets of metric space / seeking alternative proof

Published on 13 Apr 2026 - 1:09

660

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Function composition: $\Phi$ locally Lipschitz map and $f \in AC([0,1])$

Published on 17 Apr 2026 - 18:53

52

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Upper and lower limits of 'alternating' sequence

Published on 12 Apr 2026 - 4:30

454

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Continuous function times a bounded function

Published on 11 Apr 2026 - 16:03

34

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Is this a good imagination of $f$ (4.1 Remark; Rduin)

Published on 15 Apr 2026 - 16:40

100

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If $f$ is Lipschitz-continuous then $\left\lvert\int_0^1 f(x)\,dx-\frac1n\sum\limits_{k=1}^{n}f \left(\frac kn\right)\right\rvert<\frac{M}{2n}$

Published on 15 Apr 2026 - 17:57

List Question

Dedekind Cuts as a pedagogical tool

What is the value of $f(100)$?

Notation for a function with the domain $1$ or $0$?

On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

Is this an example of a pointwise convergent sequence of function but not uniformly convergent

Density of Lipschitz functions in the set of uniformly continuous functions

An inequality deduced for $-\sum_{n=1}^\infty\frac{\mu(n)}{n}x^{n-1}$ on assumption of convexity, invoking a theorem due to Dragomir

show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

How to integrate $\int{\frac{x^2+5}{x^3+3x}}dx$

Intersection of compact subsets of metric space / seeking alternative proof

Function composition: $\Phi$ locally Lipschitz map and $f \in AC([0,1])$

Upper and lower limits of 'alternating' sequence

Continuous function times a bounded function

Is this a good imagination of $f$ (4.1 Remark; Rduin)

If $f$ is Lipschitz-continuous then $\left\lvert\int_0^1 f(x)\,dx-\frac1n\sum\limits_{k=1}^{n}f \left(\frac kn\right)\right\rvert<\frac{M}{2n}$

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