List questions from real-analysis

Published on 16 Apr 2026 - 3:06

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Why do we need our set to be simple (connected) for a vector field to be gradient?

Published on 29 Apr 2026 - 12:46

24

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Finding three sequences which all converge to $0$ but satisfy a particular equation

Published on 15 Apr 2026 - 0:02

92

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How do you prove that this set is open?

Published on 01 May 2026 - 19:02

49

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Uniform convergence on closed interval.

Published on 12 Apr 2026 - 17:45

129

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Prove $|f(x) -f(y)| \le 1 \ \forall x,y$

Published on 15 Apr 2026 - 0:47

213

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Maximum ratio of L^p norms

Published on 15 Apr 2026 - 10:43

58

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If $f>0$ when does $\int_{a}^{\infty} f(x)dx$ converge/diverge?

Published on 16 Apr 2026 - 10:38

369

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Find which of the following function crosses the x-axis?

Published on 16 Apr 2026 - 2:43

69

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Prove that $([-1,1]^d,\|\cdot\|^d)$ is totally bounded.

Published on 17 Apr 2026 - 14:34

1.7k

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Prove $0\leq x \leq 1 \implies 0 \leq x^2 \leq x \leq 1 $

Published on 17 Apr 2026 - 2:40

373

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A simple way to prove that the union of non-disjoint intervals is an interval?

Published on 13 Apr 2026 - 20:53

75

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In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Published on 13 Apr 2026 - 3:08

848

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Using Fubini's theorem for Riemann integrals

Published on 10 Apr 2026 - 19:37

621

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Characterizing discontinuous derivatives

Published on 30 Apr 2026 - 19:49

List Question

Show $\int_{0}^{\infty} \sin^2{[\pi(x+\frac{1}{x})]}\,\mathrm{d}x$ diverges.

Why do we need our set to be simple (connected) for a vector field to be gradient?

Finding three sequences which all converge to $0$ but satisfy a particular equation

How do you prove that this set is open?

Uniform convergence on closed interval.

Prove $|f(x) -f(y)| \le 1 \ \forall x,y$

Maximum ratio of L^p norms

If $f>0$ when does $\int_{a}^{\infty} f(x)dx$ converge/diverge?

Find which of the following function crosses the x-axis?

Prove that $([-1,1]^d,\|\cdot\|^d)$ is totally bounded.

Prove $0\leq x \leq 1 \implies 0 \leq x^2 \leq x \leq 1 $

A simple way to prove that the union of non-disjoint intervals is an interval?

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Using Fubini's theorem for Riemann integrals

Characterizing discontinuous derivatives

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